## van Gorder, Robert Ashton

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 Author ID: van-gorder.robert-a Published as: Van Gorder, Robert A.; van Gorder, Robert A.; Van Gorder, R. A.; van Gorder, R. A. more...less Homepage: https://sites.google.com/site/ravangorder/ External Links: MGP · ORCID · Google Scholar · dblp · GND
 Documents Indexed: 193 Publications since 2008, including 1 Book 2 Contributions as Editor Co-Authors: 101 Co-Authors with 144 Joint Publications 2,824 Co-Co-Authors
all top 5

### Co-Authors

 50 single-authored 45 Vajravelu, Kuppalapalle 18 Krause, Andrew L. 11 Please, Colin P. 8 Mallory, Kristina 8 Sweet, Erik W. 7 Bhrawy, Ali Hassan 6 Baxter, Mathew 6 Choudhury, Sudipto Roy 6 Fadai, Nabil T. 6 Sloman, Benjamin M. 5 Haussermann, John 5 Planella, Ferran Brosa 5 Talay Akyildiz, F. 4 Abbasbandy, Saeid 4 Doha, Eid H. 4 Kaup, David J. 4 Kwiecinski, James A. 4 Luckins, Ellen K. 4 Oliver, James M. 4 Siginer, Dennis A. 3 Bakhtiari, Parisa 3 Bellout, Hamid 3 Sachak-Patwa, Rahil 3 Theaker, Kyle A. 2 Abdelkawy, Mohamed A. 2 Beliaev, Dmitri B. 2 Hafez, Ramy Mahmoud 2 Kim, Hyunyeon 2 Kurowski, Lawrence 2 Mahapatra, Tapas Ray 2 Nandy, Samir Kumar 2 Pop, Ioan 2 Russo, Matthew 2 Saberi Nik, Hassan 2 Waters, Sarah Louise 2 Yawar, Kamran 1 Adusumilli, Susheel 1 Akram, Zahra 1 Alofi, Abdulaziz Saleem Moslem 1 Băleanu, Dumitru I. 1 Biber, Stanisław W. 1 Birkeland, Rolf G. 1 Brennan, Joseph Patrick 1 Burton, Abigail M. 1 Cannon, John Rozier 1 Caputo, Michael R. 1 Conti, Federica 1 Effati, Sohrab 1 Eide, Ragna M. 1 Ellis, Meredith A. 1 Erban, Radek 1 Fussell, Elizabeth F. 1 González-Fariña, Raquel 1 Grindrod, Peter 1 Guilmineau, Fabien 1 Hajiketabi, Mohammad 1 Harrington, Heather A. 1 Hearns, Jessica 1 Hong, Baojian 1 Hua, Tianshu 1 Kamilova, Alissa 1 Kandel, Abraham 1 Karpenko, Daria 1 Kekić, Armin 1 Kennedy, Daniel T. 1 Khalique, Chaudry Masood 1 Kleanthous, Antigoni 1 Klika, Václav 1 Levy, Dorian 1 Li, Ronald 1 Lowry, Vanessa C. 1 Lu, Dianchen 1 Makowski, Kalie 1 Malomed, Boris A. 1 Manai, Alexandre 1 Melrose, John 1 Mesrizadeh, Mehdi 1 Mizuguchi, Hanako 1 Mohapatra, Ram Narayan 1 Mukhopadhyay, Swati 1 Münch, Andreas 1 Nevai, Andrew L. 1 Perkins, Matthew 1 Prasad, Kerehalli V. 1 Reeves, Brandon 1 Reger, K. 1 Reid, Frederick Lyall 1 Ritchie, Joshua S. 1 Ruks, Lewis 1 Saberi-Nadjafi, Jafar 1 Salas, Alvaro H. 1 Shen, Lulan 1 Shi, Borun 1 Snyder, Brooke C. 1 Taylor, Nick P. 1 Valderhaug, Aasgeir M. 1 Wu, Guocheng 1 Wu, Ruijia 1 Xu, Yifang 1 Zaky, Mahmoud A. ...and 1 more Co-Authors
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### Serials

 21 Applied Mathematics and Computation 12 Communications in Nonlinear Science and Numerical Simulation 9 Journal of Fluid Mechanics 9 Numerical Algorithms 8 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 8 Physics of Fluids 7 SIAM Journal on Applied Mathematics 7 Journal of Theoretical Biology 6 Communications in Theoretical Physics 5 Acta Mechanica 5 Mathematical Methods in the Applied Sciences 5 Bulletin of Mathematical Biology 4 Annals of Physics 4 Journal of Mathematical Chemistry 4 Nonlinear Dynamics 3 IMA Journal of Applied Mathematics 3 Journal of Mathematical Physics 3 Physica A 3 Physics Letters. A 3 Meccanica 3 Quarterly of Applied Mathematics 3 Applied Mathematics Letters 3 Archive of Applied Mechanics 3 Abstract and Applied Analysis 3 Nonlinear Analysis. Real World Applications 3 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 2 Journal of Engineering Mathematics 2 Applied Mathematics and Mechanics. (English Edition) 2 European Journal of Applied Mathematics 2 Advances in Applied Clifford Algebras 2 The Ramanujan Journal 2 Physica Scripta 2 International Mathematical Forum 2 Journal of Physics A: Mathematical and Theoretical 1 Inverse Problems 1 Journal of Computational Physics 1 Journal of Mathematical Biology 1 ZAMP. Zeitschrift für angewandte Mathematik und Physik 1 Theoretical and Computational Fluid Dynamics 1 Fuzzy Sets and Systems 1 Journal of Computational and Applied Mathematics 1 Journal of Number Theory 1 Mathematics and Computers in Simulation 1 Mechanics Research Communications 1 Quaestiones Mathematicae 1 Physica D 1 IMA Journal of Mathematical Control and Information 1 Journal of Economic Dynamics & Control 1 Applied Mathematical Modelling 1 Journal of Non-Newtonian Fluid Mechanics 1 Celestial Mechanics and Dynamical Astronomy 1 Computational and Applied Mathematics 1 Mathematical Communications 1 Differential Equations and Dynamical Systems 1 The ANZIAM Journal 1 Nonlinear Analysis. Modelling and Control 1 Mathematical Medicine and Biology 1 International Journal of Number Theory 1 Journal of Biological Dynamics 1 International Journal of Contemporary Mathematical Sciences 1 International Journal of Mathematical Analysis (Ruse) 1 Journal of Dynamics and Games 1 Proceedings A. Royal Society of London 1 Research in Number Theory
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### Fields

 85 Partial differential equations (35-XX) 59 Fluid mechanics (76-XX) 36 Ordinary differential equations (34-XX) 30 Numerical analysis (65-XX) 26 Biology and other natural sciences (92-XX) 20 Classical thermodynamics, heat transfer (80-XX) 15 Dynamical systems and ergodic theory (37-XX) 15 Statistical mechanics, structure of matter (82-XX) 8 Number theory (11-XX) 7 Quantum theory (81-XX) 5 Mechanics of deformable solids (74-XX) 5 Optics, electromagnetic theory (78-XX) 4 Sequences, series, summability (40-XX) 4 Astronomy and astrophysics (85-XX) 4 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 3 Several complex variables and analytic spaces (32-XX) 3 Systems theory; control (93-XX) 2 General and overarching topics; collections (00-XX) 2 Combinatorics (05-XX) 2 Algebraic geometry (14-XX) 2 Functions of a complex variable (30-XX) 2 Special functions (33-XX) 2 Operator theory (47-XX) 2 Calculus of variations and optimal control; optimization (49-XX) 2 Mechanics of particles and systems (70-XX) 1 Commutative algebra (13-XX) 1 Real functions (26-XX) 1 Approximations and expansions (41-XX) 1 Functional analysis (46-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Probability theory and stochastic processes (60-XX) 1 Relativity and gravitational theory (83-XX) 1 Geophysics (86-XX) 1 Information and communication theory, circuits (94-XX)

### Citations contained in zbMATH Open

155 Publications have been cited 896 times in 553 Documents Cited by Year
On the selection of auxiliary functions, operators, and convergence control parameters in the application of the homotopy analysis method to nonlinear differential equations: a general approach. Zbl 1221.65208
Van Gorder, Robert A.; Vajravelu, K.
2009
A space-time Legendre spectral tau method for the two-sided space-time Caputo fractional diffusion-wave equation. Zbl 1334.65166
Bhrawy, A. H.; Zaky, M. A.; Van Gorder, R. A.
2016
Analytic and numerical solutions to the Lane-Emden equation. Zbl 1223.85004
Van Gorder, Robert A.; Vajravelu, K.
2008
Jacobi-Gauss-Lobatto collocation method for the numerical solution of $$1+1$$ nonlinear Schrödinger equations. Zbl 1349.65511
Doha, E. H.; Bhrawy, A. H.; Abdelkawy, M. A.; Van Gorder, Robert A.
2014
Nano boundary layers over stretching surfaces. Zbl 1221.76024
Van Gorder, Robert A.; Sweet, Erik; Vajravelu, K.
2010
Existence results for third order nonlinear boundary value problems arising in nano boundary layer fluid flows over stretching surfaces. Zbl 1231.35155
Talay Akyildiz, F.; Bellout, Hamid; Vajravelu, Kuppalapalle; Van Gorder, Robert A.
2011
Gaussian waves in the Fitzhugh-Nagumo equation demonstrate one role of the auxiliary function $$H(x, t)$$ in the homotopy analysis method. Zbl 1243.35163
Van Gorder, Robert A.
2012
Control of error in the homotopy analysis of semi-linear elliptic boundary value problems. Zbl 1257.65063
Van Gorder, Robert A.
2012
Analytical solutions to a generalized Drinfel’d-Sokolov equation related to DSSH and KdV6. Zbl 1195.35271
Sweet, Erik; Van Gorder, Robert A.
2010
Nonlinear flow phenomena and homotopy analysis. Fluid flow and heat transfer. Zbl 1277.35005
Vajravelu, Kuppalapalle; Van Gorder, Robert A.
2012
Stochastic epidemic metapopulation models on networks: SIS dynamics and control strategies. Zbl 1406.92584
Krause, Andrew L.; Kurowski, Lawrence; Yawar, Kamran; Van Gorder, Robert A.
2018
Influence of curvature, growth, and anisotropy on the evolution of Turing patterns on growing manifolds. Zbl 1415.92034
Krause, Andrew L.; Ellis, Meredith A.; Van Gorder, Robert A.
2019
Implicit differential equation arising in the steady flow of a Sisko fluid. Zbl 1160.76002
Akyildiz, F. Talay; Vajravelu, K.; Mohapatra, R. N.; Sweet, Erik; van Gorder, Robert A.
2009
Optimal homotopy analysis and control of error for solutions to the non-local Whitham equation. Zbl 1299.76025
Mallory, Kristina; Van Gorder, Robert A.
2014
Shil’nikov chaos in the 4D Lorenz-Stenflo system modeling the time evolution of nonlinear acoustic-gravity waves in a rotating atmosphere. Zbl 1284.37022
Van Gorder, Robert A.
2013
A Jacobi rational pseudospectral method for Lane-Emden initial value problems arising in astrophysics on a semi-infinite interval. Zbl 1308.85006
Doha, E. H.; Bhrawy, A. H.; Hafez, R. M.; van Gorder, Robert A.
2014
Competitive modes for the Baier-Sahle hyperchaotic flow in arbitrary dimensions. Zbl 1279.34063
Saberi Nik, Hassan; van Gorder, Robert A.
2013
Classification of chaotic regimes in the T system by use of competitive modes. Zbl 1279.34056
Van Gorder, Robert A.; Choudhury, S. Roy
2010
Analytical solutions to a quasilinear differential equation related to the Lane-Emden equation of the second kind. Zbl 1270.85006
Van Gorder, Robert A.
2011
The variational iteration method is a special case of the homotopy analysis method. Zbl 1325.65118
Van Gorder, Robert A.
2015
Turing conditions for pattern forming systems on evolving manifolds. Zbl 1456.35029
Van Gorder, Robert A.; Klika, Václav; Krause, Andrew L.
2021
Emergence of chaotic regimes in the generalized Lorenz canonical form: a competitive modes analysis. Zbl 1294.34049
Van Gorder, Robert A.
2011
Existence and uniqueness results for a nonlinear differential equation arising in MHD Falkner-Skan flow. Zbl 1222.76033
Van Gorder, Robert A.; Vajravelu, K.
2010
Role of seasonality on predator-prey-subsidy population dynamics. Zbl 1343.92422
Levy, Dorian; Harrington, Heather A.; Van Gorder, Robert A.
2016
Hydromagnetic stagnation point flow of a viscous fluid over a stretching or shrinking sheet. Zbl 1293.76179
van Gorder, Robert A.; Vajravelu, K.; Pop, I.
2012
Control of error in the homotopy analysis of nonlinear Klein-Gordon initial value problems. Zbl 1286.65139
Russo, Matthew; Van Gorder, Robert A.
2013
Similarity solutions of the boundary layer equations for a nonlinearly stretching sheet. Zbl 1201.34048
Akyildiz, F. Talay; Siginer, Dennis A.; Vajravelu, K.; Cannon, J. R.; van Gorder, Robert A.
2010
Extended Stefan problem for solidification of binary alloys in a finite planar domain. Zbl 1419.80013
Brosa Planella, Ferran; Please, Colin P.; van Gorder, Robert A.
2019
Fully nonlinear local induction equation describing the motion of a vortex filament in superfluid $${^4}$$He. Zbl 1275.76042
Van Gorder, Robert A.
2012
Control of error in the homotopy analysis of solutions to the Zakharov system with dissipation. Zbl 1283.65090
Mallory, Kristina; Van Gorder, Robert A.
2013
Continuous-time dynamic games for the Cournot adjustment process for competing oligopolists. Zbl 1284.91057
Snyder, Brooke C.; Van Gorder, Robert A.; Vajravelu, K.
2013
Lane-Emden equations of second kind modelling thermal explosion in infinite cylinder and sphere. Zbl 1284.80008
Reger, K.; Van Gorder, R. A.
2013
Exponential-type solutions to a generalized Drinfel’d-Sokolov equation. Zbl 1206.37043
Sweet, Erik; Van Gorder, Robert A.
2010
Analytical and numerical solutions of the density dependent diffusion Nagumo equation. Zbl 1221.92026
Van Gorder, Robert A.; Vajravelu, K.
2008
A variational formulation of the Nagumo reaction-diffusion equation and the Nagumo telegraph equation. Zbl 1195.35010
Van Gorder, Robert A.; Vajravelu, K.
2010
Hydromagnetic stagnation point flow of a second grade fluid over a stretching sheet. Zbl 1272.76027
Van Gorder, Robert A.; Vajravelu, K.
2010
The Cauchy problem for complex fuzzy differential equations. Zbl 1315.35227
Karpenko, Daria; Van Gorder, Robert A.; Kandel, Abraham
2014
Analytical and numerical solutions of the density dependent Nagumo telegraph equation. Zbl 1201.35073
Van Gorder, Robert A.; Vajravelu, K.
2010
Analytical and numerical results for the Swift-Hohenberg equation. Zbl 1252.65178
Talay Akyildiz, F.; Siginer, Dennis A.; Vajravelu, K.; van Gorder, Robert A.
2010
Two-species migration and clustering in two-dimensional domains. Zbl 1378.92058
Kurowski, Lawrence; Krause, Andrew L.; Mizuguchi, Hanako; Grindrod, Peter; Van Gorder, Robert A.
2017
Analytical Hopf bifurcation and stability analysis of T system. Zbl 1264.34019
Van Gorder, Robert A.; Choudhury, S. Roy
2011
Predator-prey-subsidy population dynamics on stepping-stone domains. Zbl 1370.92148
Shen, Lulan; Van Gorder, Robert A.
2017
Self-similar vortex dynamics in superfluid $$^{4}He$$ under the Cartesian representation of the Hall-Vinen model including superfluid friction. Zbl 1320.76015
Van Gorder, Robert A.
2013
A general class of coupled nonlinear differential equations arising in self-similar solutions of convective heat transfer problems. Zbl 1211.34037
Van Gorder, Robert A.; Vajravelu, K.
2010
Multiple solutions for hydromagnetic flow of a second grade fluid over a stretching or shrinking sheet. Zbl 1329.76049
Van Gorder, Robert A.; Vajravelu, K.
2011
Asymptotic analysis of a silicon furnace model. Zbl 1394.80009
Sloman, Benjamin M.; Please, Colin P.; van Gorder, Robert A.
2018
Painlevé property and exact solutions for a nonlinear wave equation with generalized power-law nonlinearities. Zbl 1277.35102
Russo, Matthew; Van Gorder, Robert A.; Choudhury, S. Roy
2013
Reproducing kernel method for the numerical solution of the Brinkman-Forchheimer momentum equation. Zbl 1382.65459
Abbasbandy, S.; van Gorder, R. A.; Bakhtiari, P.
2017
On the choice of auxiliary linear operator in the optimal homotopy analysis of the Cahn-Hilliard initial value problem. Zbl 1293.65137
Baxter, Mathew; van Gorder, Robert A.; Vajravelu, Kuppalapalle
2014
Motion of a helical vortex filament in superfluid $$^{4}He$$ under the extrinsic form of the local induction approximation. Zbl 1320.76028
Van Gorder, Robert A.
2013
Traveling wave solutions of the $$n$$-dimensional coupled Yukawa equations. Zbl 1246.35170
Van Gorder, Robert A.
2012
Existence and uniqueness results for a nonlinear differential equation arising in viscous flow over a nonlinearly stretching sheet. Zbl 1229.34041
Van Gorder, Robert A.; Vajravelu, K.; Akyildiz, F. Talay
2011
Chaotic regimes, post-bifurcation dynamics, and competitive modes for a generalized double Hopf normal form. Zbl 1258.34082
Reeves, Brandon; Van Gorder, Robert A.; Choudhury, S. Roy
2012
Analytical solutions of a coupled nonlinear system arising in a flow between stretching disks. Zbl 1277.76024
Van Gorder, Robert A.; Sweet, Erik; Vajravelu, K.
2010
High-order nonlinear boundary value problems admitting multiple exact solutions with application to the fluid flow over a sheet. Zbl 1425.35164
Van Gorder, Robert A.
2010
Helical vortex filament motion under the non-local Biot-Savart model. Zbl 1335.76015
Van Gorder, Robert A.
2015
Dynamics of the Rayleigh-plesset equation modelling a gas-filled bubble immersed in an incompressible fluid. Zbl 1383.76481
Van Gorder, Robert A.
2016
Motion of a vortex filament in the local induction approximation: a perturbative approach. Zbl 1291.76075
van Gorder, Robert A.
2012
General rotating quantum vortex filaments in the low-temperature Svistunov model of the local induction approximation. Zbl 1321.82041
Van Gorder, Robert A.
2014
Stability of auxiliary linear operator and convergence-control parameter in the homotopy analysis method. Zbl 1308.35018
Van Gorder, Robert A.
2014
The chaotic Dadras-Momeni system: control and hyperchaotification. Zbl 1397.49026
Saberi Nik, Hassan; Van Gorder, Robert A.; Gambino, G.
2016
A non-local cross-diffusion model of population dynamics II: exact, approximate, and numerical traveling waves in single- and multi-species populations. Zbl 1448.92212
Krause, Andrew L.; Van Gorder, Robert A.
2020
Squared eigenfunctions and the perturbation theory for the nondegenerate $$N \times N$$ operator: a general outline. Zbl 1202.81069
Kaup, D. J.; Van Gorder, Robert A.
2010
The inverse scattering transform and squared eigenfunctions for the nondegenerate $$3 \times 3$$ operator and its soliton structure. Zbl 1204.47011
Kaup, D. J.; van Gorder, Robert A.
2010
Envelope theorems for locally differentiable open-loop Stackelberg equilibria of finite horizon differential games. Zbl 1230.91021
Van Gorder, Robert A.; Caputo, Michael R.
2010
Diffusive instabilities and spatial patterning from the coupling of reaction-diffusion processes with Stokes flow in complex domains. Zbl 1430.76176
Van Gorder, Robert A.; Kim, Hyunyeon; Krause, Andrew L.
2019
Homogenization of a shrinking core model for gas-solid reactions in granular particles. Zbl 1461.35029
Sloman, Benjamin M.; Please, Colin P.; Van Gorder, Robert A.
2019
Nonlinear dynamics of discrete time multi-level leader-follower games. Zbl 1427.91069
Wu, Ruijia; Van Gorder, Robert A.
2018
Does the Riemann zeta function satisfy a differential equation? Zbl 1382.11060
Van Gorder, Robert A.
2015
Predator-prey-subsidy population dynamics on stepping-stone domains with dispersal delays. Zbl 1397.92568
Eide, Ragna M.; Krause, Andrew L.; Fadai, Nabil T.; Van Gorder, Robert A.
2018
Glaisher-type products over the primes. Zbl 1245.40003
Van Gorder, Robert A.
2012
Method for constructing analytical solutions to the Dym initial value problem. Zbl 1354.35131
Mallory, Kristina; Van Gorder, Robert A.
2014
Multicomplex wave functions for linear and nonlinear Schrödinger equations. Zbl 1369.30065
Theaker, Kyle A.; Van Gorder, Robert A.
2017
Self-similar vortex filament motion under the non-local Biot-Savart model. Zbl 1462.76007
van Gorder, Robert A.
2016
Several types of similarity solutions for the Hunter-Saxton equation. Zbl 1319.35110
Baxter, Mathew; van Gorder, Robert A.; Vajravelu, Kuppalapalle
2015
Response to “Comment on ‘Motion of a helical vortex filament in superfluid $$^{4}$$He under the extrinsic form of the local induction approximation{’}” [Phys. Fluids 26, Paper No. 019101 (2014)]. Zbl 1321.76016
Van Gorder, Robert A.
2014
Exact and analytical solutions for a nonlinear sigma model. Zbl 1383.35187
Baxter, Mathew; Van Gorder, Robert A.
2014
Melting and dripping of a heated material with temperature-dependent viscosity in a thin vertical tube. Zbl 1460.80014
Sloman, Benjamin M.; Please, Colin P.; Van Gorder, Robert A.
2020
A transformed time-dependent Michaelis-Menten enzymatic reaction model and its asymptotic stability. Zbl 1311.92072
Mallory, Kristina; Van Gorder, Robert A.
2014
A non-local cross-diffusion model of population dynamics I: emergent spatial and spatiotemporal patterns. Zbl 1448.92253
Taylor, Nick P.; Kim, Hyunyeon; Krause, Andrew L.; Van Gorder, Robert A.
2020
Third-order partial differential equations arising in the impulsive motion of a flat plate. Zbl 1221.74053
Van Gorder, Robert A.; Vajravelu, K.
2009
Computing the region of convergence for power series in many real variables: A ratio-like test. Zbl 1252.65064
Van Gorder, Robert A.
2011
Convective heat transfer in a conducting fluid over a permeable stretching surface with suction and internal heat generation/absorption. Zbl 1388.76349
Van Gorder, Robert A.; Vajravelu, K.
2011
Natural convection heat transfer of a viscous fluid in a vertical porous channel. Zbl 1254.76132
Akyildiz, F. Talay; Siginer, Dennis A.; Vajravelu, K.; Van Gorder, Robert A.
2012
Trigonometric and hyperbolic type solutions to a generalized Drinfel’d-Sokolov equation. Zbl 1206.35223
Sweet, Erik; Van Gorder, Robert A.
2010
Existence and uniqueness results for a nonlinear differential equation arising in stagnation point flow in a porous medium. Zbl 1397.76142
Van Gorder, Robert A.; Vajravelu, Kuppalapalle
2010
Exact and analytic solutions of the ernst equation governing axially symmetric stationary vacuum gravitational fields. Zbl 1266.83017
Baxter, Mathew; Van Gorder, Robert A.
2013
Jacobi rational-Gauss collocation method for Lane-Emden equations of astrophysical significance. Zbl 1423.85007
Doha, Eid H.; Bhrawy, Ali H.; Hafez, Ramy M.; Van Gorder, Robert A.
2014
Hybrid approach to modeling spatial dynamics of systems with generalist predators. Zbl 1406.92661
Fussell, Elizabeth F.; Krause, Andrew L.; Van Gorder, Robert A.
2019
An efficient collocation method for a class of boundary value problems arising in mathematical physics and geometry. Zbl 1470.65141
Bhrawy, A. H.; Alofi, A. S.; Van Gorder, R. A.
2014
Non-local dynamics governing the self-induced motion of a planar vortex filament. Zbl 1326.76035
Van Gorder, Robert A.
2015
Asymptotic analysis of a multiphase drying model motivated by coffee bean roasting. Zbl 1386.80005
2018
The Biot-Savart description of Kelvin waves on a quantum vortex filament in the presence of mutual friction and a driving fluid. Zbl 1371.76168
Van Gorder, Robert A.
2015
On the utility of the homotopy analysis method for non-analytic and global solutions to nonlinear differential equations. Zbl 1375.65103
Van Gorder, Robert A.
2017
Solutions to a novel Casimir equation for the Itô system. Zbl 1247.35065
Van Gorder, Robert A.
2011
A linearization approach for rational nonlinear models in mathematical physics. Zbl 1247.34020
Van Gorder, Robert A.
2012
Turing and Benjamin-Feir instability mechanisms in non-autonomous systems. Zbl 1472.35221
van Gorder, Robert A.
2020
Erratum to: “Existence and uniqueness results for a nonlinear differential equation arising in stagnation point flow in a porous medium”. Zbl 1401.76144
Van Gorder, Robert A.; Vajravelu, Kuppalapalle
2012
Chemically reactive solute transfer in a moving fluid over a moving surface. Zbl 1401.76162
Mukhopadhyay, Swati; Vajravelu, Kuppalapalle; Van Gorder, Robert A.
2013
A note on flow geometries and the similarity solutions of the boundary layer equations for a nonlinearly stretching sheet. Zbl 1271.76068
Van Gorder, Robert A.; Vajravelu, Kuppalapalle
2010
Turing conditions for pattern forming systems on evolving manifolds. Zbl 1456.35029
Van Gorder, Robert A.; Klika, Václav; Krause, Andrew L.
2021
A non-local cross-diffusion model of population dynamics II: exact, approximate, and numerical traveling waves in single- and multi-species populations. Zbl 1448.92212
Krause, Andrew L.; Van Gorder, Robert A.
2020
Melting and dripping of a heated material with temperature-dependent viscosity in a thin vertical tube. Zbl 1460.80014
Sloman, Benjamin M.; Please, Colin P.; Van Gorder, Robert A.
2020
A non-local cross-diffusion model of population dynamics I: emergent spatial and spatiotemporal patterns. Zbl 1448.92253
Taylor, Nick P.; Kim, Hyunyeon; Krause, Andrew L.; Van Gorder, Robert A.
2020
Turing and Benjamin-Feir instability mechanisms in non-autonomous systems. Zbl 1472.35221
van Gorder, Robert A.
2020
Modeling microsilica particle formation and growth due to the combustion reaction of silicon monoxide with oxygen. Zbl 1447.35055
González-Fariña, Raquel; Münch, Andreas; Oliver, James M.; van Gorder, Robert A.
2020
Influence of temperature on Turing pattern formation. Zbl 1472.35410
van Gorder, Robert A.
2020
Perturbation theory for Bose-Einstein condensates on bounded space domains. Zbl 1472.81098
van Gorder, Robert A.
2020
Unstaggered-staggered solitons on one- and two-dimensional two-component discrete nonlinear Schrödinger lattices. Zbl 1453.82047
Van Gorder, Robert A.; Krause, Andrew L.; Malomed, Boris A.; Kaup, D. J.
2020
Influence of curvature, growth, and anisotropy on the evolution of Turing patterns on growing manifolds. Zbl 1415.92034
Krause, Andrew L.; Ellis, Meredith A.; Van Gorder, Robert A.
2019
Extended Stefan problem for solidification of binary alloys in a finite planar domain. Zbl 1419.80013
Brosa Planella, Ferran; Please, Colin P.; van Gorder, Robert A.
2019
Diffusive instabilities and spatial patterning from the coupling of reaction-diffusion processes with Stokes flow in complex domains. Zbl 1430.76176
Van Gorder, Robert A.; Kim, Hyunyeon; Krause, Andrew L.
2019
Homogenization of a shrinking core model for gas-solid reactions in granular particles. Zbl 1461.35029
Sloman, Benjamin M.; Please, Colin P.; Van Gorder, Robert A.
2019
Hybrid approach to modeling spatial dynamics of systems with generalist predators. Zbl 1406.92661
Fussell, Elizabeth F.; Krause, Andrew L.; Van Gorder, Robert A.
2019
Optimal homotopy analysis and control of error for implicitly defined fully nonlinear differential equations. Zbl 1416.65251
Van Gorder, Robert A.
2019
Turing instability and colony formation in spatially extended Rosenzweig-MacArthur predator-prey models with allochthonous resources. Zbl 1430.92082
Zhou, Zhi; Van Gorder, Robert A.
2019
The role of network structure and time delay in a metapopulation Wilson-Cowan model. Zbl 1416.92007
Conti, Federica; Van Gorder, Robert A.
2019
Amplitude death criteria for coupled complex Ginzburg-Landau systems. Zbl 1430.35221
Van Gorder, Robert A.; Krause, Andrew L.; Kwiecinski, James A.
2019
A homogenization approach for the roasting of an array of coffee beans. Zbl 1419.80016
Sachak-Patwa, Rahil; Fadai, Nabil; van Gorder, Robert A.
2019
Chaotic rotations of a rigid ellipsoidal body exhibiting spin-orbit misalignment in a periodic orbit. Zbl 1423.70054
Kwiecinski, James A.; Biber, Stanisław W.; Van Gorder, Robert A.
2019
Stochastic epidemic metapopulation models on networks: SIS dynamics and control strategies. Zbl 1406.92584
Krause, Andrew L.; Kurowski, Lawrence; Yawar, Kamran; Van Gorder, Robert A.
2018
Asymptotic analysis of a silicon furnace model. Zbl 1394.80009
Sloman, Benjamin M.; Please, Colin P.; van Gorder, Robert A.
2018
Nonlinear dynamics of discrete time multi-level leader-follower games. Zbl 1427.91069
Wu, Ruijia; Van Gorder, Robert A.
2018
Predator-prey-subsidy population dynamics on stepping-stone domains with dispersal delays. Zbl 1397.92568
Eide, Ragna M.; Krause, Andrew L.; Fadai, Nabil T.; Van Gorder, Robert A.
2018
Asymptotic analysis of a multiphase drying model motivated by coffee bean roasting. Zbl 1386.80005
2018
Instability in the self-similar motion of a planar solidification front. Zbl 1408.80004
Brosa Planella, Ferran; Please, Colin P.; Van Gorder, Robert A.
2018
Bose-Einstein condensation under the cubic-quintic Gross-Pitaevskii equation in radial domains. Zbl 1382.35272
Luckins, Ellen K.; Van Gorder, Robert A.
2018
Coupled complex Ginzburg-Landau systems with saturable nonlinearity and asymmetric cross-phase modulation. Zbl 1398.35222
Van Gorder, Robert A.; Krause, Andrew L.; Brosa Planella, Ferran; Burton, Abigail M.
2018
Dynamics of nearly parallel interacting vortex filaments. Zbl 1421.76048
Kwiecinski, James A.; Van Gorder, Robert A.
2018
Reproducing kernel method for the numerical solution of the 1D Swift-Hohenberg equation. Zbl 1429.65262
Bakhtiari, P.; Abbasbandy, S.; Van Gorder, R. A.
2018
Bifurcations and dynamics emergent from lattice and continuum models of bioactive porous media. Zbl 1402.35285
Krause, Andrew L.; Beliaev, Dmitry; Van Gorder, Robert A.; Waters, Sarah L.
2018
Chaotic dynamics in the planar gravitational many-body problem with rigid body rotations. Zbl 1390.70021
Kwiecinski, James A.; Kovacs, Attila; Krause, Andrew L.; Planella, Ferran Brosa; Van Gorder, Robert A.
2018
Solving the Dym initial value problem in reproducing kernel space. Zbl 1393.65038
Bakhtiari, P.; Abbasbandy, S.; Van Gorder, R. A.
2018
Understanding viral video dynamics through an epidemic modelling approach. Zbl 07549580
Sachak-Patwa, Rahil; Fadai, Nabil T.; Van Gorder, Robert A.
2018
Two-species migration and clustering in two-dimensional domains. Zbl 1378.92058
Kurowski, Lawrence; Krause, Andrew L.; Mizuguchi, Hanako; Grindrod, Peter; Van Gorder, Robert A.
2017
Predator-prey-subsidy population dynamics on stepping-stone domains. Zbl 1370.92148
Shen, Lulan; Van Gorder, Robert A.
2017
Reproducing kernel method for the numerical solution of the Brinkman-Forchheimer momentum equation. Zbl 1382.65459
Abbasbandy, S.; van Gorder, R. A.; Bakhtiari, P.
2017
Multicomplex wave functions for linear and nonlinear Schrödinger equations. Zbl 1369.30065
Theaker, Kyle A.; Van Gorder, Robert A.
2017
On the utility of the homotopy analysis method for non-analytic and global solutions to nonlinear differential equations. Zbl 1375.65103
Van Gorder, Robert A.
2017
Hyperchaos from a model of coupled stratosphere-troposphere dynamics. Zbl 1362.34073
Adusumilli, Susheel; Van Gorder, Robert A.
2017
Asymptotic solutions for a relativistic formulation of the generalized nonextensive Thomas-Fermi model. Zbl 1364.82007
Lowry, Vanessa C.; Van Gorder, Robert A.
2017
On the inverse problem of competitive modes and the search for chaotic dynamics. Zbl 1380.37074
Ruks, Lewis; Van Gorder, Robert A.
2017
A space-time Legendre spectral tau method for the two-sided space-time Caputo fractional diffusion-wave equation. Zbl 1334.65166
Bhrawy, A. H.; Zaky, M. A.; Van Gorder, R. A.
2016
Role of seasonality on predator-prey-subsidy population dynamics. Zbl 1343.92422
Levy, Dorian; Harrington, Heather A.; Van Gorder, Robert A.
2016
Dynamics of the Rayleigh-plesset equation modelling a gas-filled bubble immersed in an incompressible fluid. Zbl 1383.76481
Van Gorder, Robert A.
2016
The chaotic Dadras-Momeni system: control and hyperchaotification. Zbl 1397.49026
Saberi Nik, Hassan; Van Gorder, Robert A.; Gambino, G.
2016
Self-similar vortex filament motion under the non-local Biot-Savart model. Zbl 1462.76007
van Gorder, Robert A.
2016
Jacobi-Gauss-Lobatto collocation method for solving nonlinear reaction-diffusion equations subject to Dirichlet boundary conditions. Zbl 1446.65124
Bhrawy, A. H.; Doha, E. H.; Abdelkawy, M. A.; Van Gorder, Robert A.
2016
The variational iteration method is a special case of the homotopy analysis method. Zbl 1325.65118
Van Gorder, Robert A.
2015
Helical vortex filament motion under the non-local Biot-Savart model. Zbl 1335.76015
Van Gorder, Robert A.
2015
Does the Riemann zeta function satisfy a differential equation? Zbl 1382.11060
Van Gorder, Robert A.
2015
Several types of similarity solutions for the Hunter-Saxton equation. Zbl 1319.35110
Baxter, Mathew; van Gorder, Robert A.; Vajravelu, Kuppalapalle
2015
Non-local dynamics governing the self-induced motion of a planar vortex filament. Zbl 1326.76035
Van Gorder, Robert A.
2015
The Biot-Savart description of Kelvin waves on a quantum vortex filament in the presence of mutual friction and a driving fluid. Zbl 1371.76168
Van Gorder, Robert A.
2015
Competitive modes for the detection of chaotic parameter regimes in the general chaotic bilinear system of Lorenz type. Zbl 1314.34092
Mallory, Kristina; Van Gorder, Robert A.
2015
Zero curvature representation, bi-Hamiltonian structure, and an integrable hierarchy for the Zakharov-Ito system. Zbl 1318.37012
Baxter, Mathew; Choudhury, S. Roy; Van Gorder, Robert A.
2015
Existence and numerical simulation of periodic traveling wave solutions to the Casimir equation for the Itô system. Zbl 1457.35050
Abbasbandy, S.; Van Gorder, R. A.; Hajiketabi, M.; Mesrizadeh, M.
2015
Bounds, monotonicity, uniqueness, and analytical calculation of a class of similarity solutions for the fluid flow over a nonlinearly stretching sheet. Zbl 1323.34034
van Gorder, Robert A.
2015
Translation of waves along quantum vortex filaments in the low-temperature two-dimensional local induction approximation. Zbl 1326.82026
Van Gorder, Robert A.
2015
Jacobi-Gauss-Lobatto collocation method for the numerical solution of $$1+1$$ nonlinear Schrödinger equations. Zbl 1349.65511
Doha, E. H.; Bhrawy, A. H.; Abdelkawy, M. A.; Van Gorder, Robert A.
2014
Optimal homotopy analysis and control of error for solutions to the non-local Whitham equation. Zbl 1299.76025
Mallory, Kristina; Van Gorder, Robert A.
2014
A Jacobi rational pseudospectral method for Lane-Emden initial value problems arising in astrophysics on a semi-infinite interval. Zbl 1308.85006
Doha, E. H.; Bhrawy, A. H.; Hafez, R. M.; van Gorder, Robert A.
2014
The Cauchy problem for complex fuzzy differential equations. Zbl 1315.35227
Karpenko, Daria; Van Gorder, Robert A.; Kandel, Abraham
2014
On the choice of auxiliary linear operator in the optimal homotopy analysis of the Cahn-Hilliard initial value problem. Zbl 1293.65137
Baxter, Mathew; van Gorder, Robert A.; Vajravelu, Kuppalapalle
2014
General rotating quantum vortex filaments in the low-temperature Svistunov model of the local induction approximation. Zbl 1321.82041
Van Gorder, Robert A.
2014
Stability of auxiliary linear operator and convergence-control parameter in the homotopy analysis method. Zbl 1308.35018
Van Gorder, Robert A.
2014
Method for constructing analytical solutions to the Dym initial value problem. Zbl 1354.35131
Mallory, Kristina; Van Gorder, Robert A.
2014
Response to “Comment on ‘Motion of a helical vortex filament in superfluid $$^{4}$$He under the extrinsic form of the local induction approximation{’}” [Phys. Fluids 26, Paper No. 019101 (2014)]. Zbl 1321.76016
Van Gorder, Robert A.
2014
Exact and analytical solutions for a nonlinear sigma model. Zbl 1383.35187
Baxter, Mathew; Van Gorder, Robert A.
2014
A transformed time-dependent Michaelis-Menten enzymatic reaction model and its asymptotic stability. Zbl 1311.92072
Mallory, Kristina; Van Gorder, Robert A.
2014
Jacobi rational-Gauss collocation method for Lane-Emden equations of astrophysical significance. Zbl 1423.85007
Doha, Eid H.; Bhrawy, Ali H.; Hafez, Ramy M.; Van Gorder, Robert A.
2014
An efficient collocation method for a class of boundary value problems arising in mathematical physics and geometry. Zbl 1470.65141
Bhrawy, A. H.; Alofi, A. S.; Van Gorder, R. A.
2014
Hybrid projective synchronization and control of the baier-sahle hyperchaotic flow in arbitrary dimensions with unknown parameters. Zbl 1338.93304
Saberi Nik, H.; Saberi-Nadjafi, J.; Effati, S.; van Gorder, R. A.
2014
Decay of helical Kelvin waves on a quantum vortex filament. Zbl 1323.82056
Van Gorder, Robert A.
2014
Classification of two types of weak solutions to the Casimir equation for the Itō system. Zbl 1298.35171
Haussermann, John; van Gorder, Robert A.
2014
Solution method for the transformed time-dependent Michaelis-Menten enzymatic reaction model. Zbl 1331.92061
Li, Ronald; van Gorder, Robert A.; Mallory, Kristina; Vajravelu, Kuppalapalle
2014
Response to “Comment on ‘General rotating quantum vortex filaments in the low-temperature Svistunov model of the local induction approximation{’}” [Phys. Fluids 26, Paper No. 119101 (2014)]. Zbl 1323.82057
Van Gorder, Robert A.
2014
Several classes of exact solutions to the 1+1 Born-Infeld equation. Zbl 1457.78004
Mallory, Kristina; Van Gorder, Robert A.; Vajravelu, Kuppalapalle
2014
Computing semi-commuting differential operators in one and multiple variables. Zbl 1312.13031
Van Gorder, Robert A.
2014
Shil’nikov chaos in the 4D Lorenz-Stenflo system modeling the time evolution of nonlinear acoustic-gravity waves in a rotating atmosphere. Zbl 1284.37022
Van Gorder, Robert A.
2013
Competitive modes for the Baier-Sahle hyperchaotic flow in arbitrary dimensions. Zbl 1279.34063
Saberi Nik, Hassan; van Gorder, Robert A.
2013
Control of error in the homotopy analysis of nonlinear Klein-Gordon initial value problems. Zbl 1286.65139
Russo, Matthew; Van Gorder, Robert A.
2013
Control of error in the homotopy analysis of solutions to the Zakharov system with dissipation. Zbl 1283.65090
Mallory, Kristina; Van Gorder, Robert A.
2013
Continuous-time dynamic games for the Cournot adjustment process for competing oligopolists. Zbl 1284.91057
Snyder, Brooke C.; Van Gorder, Robert A.; Vajravelu, K.
2013
Lane-Emden equations of second kind modelling thermal explosion in infinite cylinder and sphere. Zbl 1284.80008
Reger, K.; Van Gorder, R. A.
2013
Self-similar vortex dynamics in superfluid $$^{4}He$$ under the Cartesian representation of the Hall-Vinen model including superfluid friction. Zbl 1320.76015
Van Gorder, Robert A.
2013
Painlevé property and exact solutions for a nonlinear wave equation with generalized power-law nonlinearities. Zbl 1277.35102
Russo, Matthew; Van Gorder, Robert A.; Choudhury, S. Roy
2013
Motion of a helical vortex filament in superfluid $$^{4}He$$ under the extrinsic form of the local induction approximation. Zbl 1320.76028
Van Gorder, Robert A.
2013
Exact and analytic solutions of the ernst equation governing axially symmetric stationary vacuum gravitational fields. Zbl 1266.83017
Baxter, Mathew; Van Gorder, Robert A.
2013
Chemically reactive solute transfer in a moving fluid over a moving surface. Zbl 1401.76162
Mukhopadhyay, Swati; Vajravelu, Kuppalapalle; Van Gorder, Robert A.
2013
A multicomplex Riemann zeta function. Zbl 1262.30058
Reid, Frederick Lyall; Van Gorder, Robert A.
2013
Hyper-Riccati equations and integrable reductions permitting stationary solutions for complex hyperbolic field equations. Zbl 1293.34018
Theaker, Kyle A.; Van Gorder, Robert A.
2013
Gaussian waves in the Fitzhugh-Nagumo equation demonstrate one role of the auxiliary function $$H(x, t)$$ in the homotopy analysis method. Zbl 1243.35163
Van Gorder, Robert A.
2012
Control of error in the homotopy analysis of semi-linear elliptic boundary value problems. Zbl 1257.65063
Van Gorder, Robert A.
2012
Nonlinear flow phenomena and homotopy analysis. Fluid flow and heat transfer. Zbl 1277.35005
Vajravelu, Kuppalapalle; Van Gorder, Robert A.
2012
Hydromagnetic stagnation point flow of a viscous fluid over a stretching or shrinking sheet. Zbl 1293.76179
van Gorder, Robert A.; Vajravelu, K.; Pop, I.
2012
Fully nonlinear local induction equation describing the motion of a vortex filament in superfluid $${^4}$$He. Zbl 1275.76042
Van Gorder, Robert A.
2012
Traveling wave solutions of the $$n$$-dimensional coupled Yukawa equations. Zbl 1246.35170
Van Gorder, Robert A.
2012
Chaotic regimes, post-bifurcation dynamics, and competitive modes for a generalized double Hopf normal form. Zbl 1258.34082
Reeves, Brandon; Van Gorder, Robert A.; Choudhury, S. Roy
2012
Motion of a vortex filament in the local induction approximation: a perturbative approach. Zbl 1291.76075
van Gorder, Robert A.
2012
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