## ode23

 swMATH ID: 6600 Software Authors: MathWorks, Inc Description: The MATLAB ODE Suite: ode23: Solve nonstiff differential equations; low order method. [T,Y] = solver(odefun,tspan,y0) with tspan = [t0 tf] integrates the system of differential equations y′ = f(t,y) from time t0 to tf with initial conditions y0. The first input argument, odefun, is a function handle. The function, f = odefun(t,y), for a scalar t and a column vector y, must return a column vector f corresponding to f(t,y). Each row in the solution array Y corresponds to a time returned in column vector T. To obtain solutions at the specific times t0, t1,...,tf (all increasing or all decreasing), use tspan = [t0,t1,...,tf]. Parameterizing Functions explains how to provide additional parameters to the function fun, if necessary. [T,Y] = solver(odefun,tspan,y0,options) solves as above with default integration parameters replaced by property values specified in options, an argument created with the odeset function. Commonly used properties include a scalar relative error tolerance RelTol (1e-3 by default) and a vector of absolute error tolerances AbsTol (all components are 1e-6 by default). If certain components of the solution must be nonnegative, use the odeset function to set the NonNegative property to the indices of these components. See odeset for details. [T,Y,TE,YE,IE] = solver(odefun,tspan,y0,options) solves as above while also finding where functions of (t,y), called event functions, are zero. For each event function, you specify whether the integration is to terminate at a zero and whether the direction of the zero crossing matters. Do this by setting the ’Events’ property to a function, e.g., events or @events, and creating a function [value,isterminal,direction] = events(t,y). For the ith event function in events,value(i) is the value of the function. isterminal(i) = 1, if the integration is to terminate at a zero of this event function and 0 otherwise. direction(i) = 0 if all zeros are to be computed (the default), +1 if only the zeros where the event function increases, and -1 if only the zeros where the event function decreases. Corresponding entries in TE, YE, and IE return, respectively, the time at which an event occurs, the solution at the time of the event, and the index i of the event function that vanishes. Homepage: http://www.mathworks.de/de/help/matlab/ref/ode23.html Dependencies: Matlab Related Software: Matlab; MATLAB ODE suite; ode45; ode23s; ode113; Ode15s; RODAS; bvp4c; Simulink; VODE; DIMSIM; KELLEY; GitHub; ODEPACK; dde23; SUNDIALS; Chebfun; Maple; Differentiation Matrix Suite; LSODE Cited in: 341 Publications Further Publications: http://epubs.siam.org/doi/abs/10.1137/S1064827594276424
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### Cited by 698 Authors

 13 Shampine, Lawrence Fred 12 Weiner, Rüdiger 8 Abdi, Ali 8 Jackiewicz, Zdzislaw 6 Hojjati, Gholamreza 6 Kulikov, Gennady Yur’evich 6 Montijano, Juan Ignacio 6 Rández, Luis 5 Calvo, Manuel 5 Dutykh, Denys 5 Fazio, Riccardo 5 Kanwar, Vinay 5 Podhaisky, Helmut 5 Singh, Gurjinder 4 Dehghan Takht Fooladi, Mehdi 4 Gobbert, Matthias K. 4 Lambers, James V. 4 Luo, Xinlong 4 Ramos, Higinio 4 Thompson, Sylvester 3 Almeida, Rui M. P. 3 Bhatia, Saurabh 3 Bowling, Alan P. 3 Byrne, Helen Mary 3 Chatterjee, Abhishek 3 Corless, Robert Malcolm 3 Günther, Michael 3 Kelley, Carl T. 3 Kopecz, Stefan 3 Laburta, María Pilar 3 Lamba, Harbir 3 Meister, Andreas 3 Meli, Enrico 3 Sabouri, Mania 3 Simpson, Matthew J. 3 Soleimani, Behnam 3 Stuart, Andrew M. 3 Tyson, Rebecca C. 3 Zubik-Kowal, Barbara 2 Abelman, Shirley 2 Antontsev, Stanislav Nikolaevich 2 Aoki, Yasunori 2 Barbieri, Luca 2 Bartel, Andreas 2 Bensow, Rickard E. 2 Bertaccini, Daniele 2 Buccella, Giacomo 2 Chiavazzo, Eliodoro 2 Clamond, Didier 2 Conte, Dajana 2 Cuomo, Salvatore 2 Duchêne, Vincent 2 Duque, José C. M. 2 Eberhard, Peter 2 Enright, Wayne H. 2 Gaffney, Eamonn A. 2 Ghahramani, Ebrahim 2 Giannino, Francesco 2 Guimarães, Osvaldo 2 Hayami, Ken 2 Iacono, Salvatore 2 Ibrahim, Zarina Bibi Binti 2 Iyaniwura, Sarafa A. 2 Jannelli, Alessandra 2 Joly, Marcel 2 Judd, Kevin 2 Klinge, Marcel 2 Kolev, Mikhail K. 2 Konagaya, Akihiko 2 Kvaerno, Anne 2 Lane, W. D. 2 Liao, Li-Zhi 2 Maini, Philip Kumar 2 Malgesini, Roberto 2 Montagu, E. L. 2 Norbury, John W. 2 Novati, Paolo 2 Othman, Khairil Iskandar 2 Piqueira, José Roberto Castilho 2 Plank, Michael J. 2 Ridolfi, Alessandro 2 Russo, Lucia 2 Sandu, Adrian 2 Schmitt, Bernhard A. 2 Shadid, John N. 2 Siettos, Constantinos I. 2 Small, Michael 2 Soheili, Ali Reza 2 Suleiman, Mohamed Bin 2 Towne, Aaron 2 Trendafilov, Nickolay T. 2 Van Daele, Marnix 2 Villa, Andrea 2 Walker, Benjamin J. 2 Ward, Michael J. 2 Wilson, James B. 2 Yatim, S. A. M. 1 Abbiati, Roberto Andrea 1 Aceituno, Javier F. 1 Adekanye, Oluwaseye ...and 598 more Authors
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### Cited in 122 Serials

 28 Applied Numerical Mathematics 24 Journal of Computational and Applied Mathematics 17 Journal of Theoretical Biology 14 Applied Mathematics and Computation 11 Computers & Mathematics with Applications 10 Applied Mathematical Modelling 9 Journal of Computational Physics 9 Multibody System Dynamics 8 Journal of Fluid Mechanics 8 BIT 8 Mathematical Problems in Engineering 7 Numerical Algorithms 6 Journal of Mathematical Biology 6 SIAM Journal on Scientific Computing 5 Computer Methods in Applied Mechanics and Engineering 5 Mathematical and Computer Modelling 5 Journal of Scientific Computing 4 Physica D 4 Computational and Applied Mathematics 4 Communications in Nonlinear Science and Numerical Simulation 3 Acta Mechanica 3 Computers and Fluids 3 Journal of Engineering Mathematics 3 Mathematical Biosciences 3 Mathematical Methods in the Applied Sciences 3 Bulletin of Mathematical Biology 3 Chaos, Solitons and Fractals 3 Calcolo 3 Journal of Differential Equations 3 Linear Algebra and its Applications 3 Celestial Mechanics and Dynamical Astronomy 3 Nonlinear Dynamics 3 Nonlinear Analysis. Real World Applications 2 Physica A 2 Mathematics of Computation 2 Journal of Optimization Theory and Applications 2 Mathematics and Computers in Simulation 2 Meccanica 2 SIAM Journal on Numerical Analysis 2 Theoretical Population Biology 2 Journal of the Nigerian Mathematical Society 2 Computational Mechanics 2 European Journal of Applied Mathematics 2 Computational Mathematics and Mathematical Physics 2 SIAM Review 2 Computational Statistics and Data Analysis 2 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 2 Journal of Mathematical Chemistry 2 Differential Equations and Dynamical Systems 2 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 2 Mathematical Biosciences and Engineering 1 Computer Physics Communications 1 International Journal of Heat and Mass Transfer 1 International Journal of Solids and Structures 1 Journal of the Franklin Institute 1 Journal of Mathematical Physics 1 Journal of the Mechanics and Physics of Solids 1 Journal of Statistical Physics 1 Physics Letters. A 1 Wave Motion 1 Theoretical and Computational Fluid Dynamics 1 ACM Transactions on Mathematical Software 1 Automatica 1 Information Sciences 1 International Journal for Numerical Methods in Engineering 1 Journal of the Korean Mathematical Society 1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 1 Numerische Mathematik 1 Ricerche di Matematica 1 Studies in Applied Mathematics 1 Acta Applicandae Mathematicae 1 Bulletin of the Iranian Mathematical Society 1 Optimization 1 New Generation Computing 1 Numerical Methods for Partial Differential Equations 1 Annals of Operations Research 1 European Journal of Operational Research 1 Pattern Recognition 1 Journal of Nonlinear Science 1 Continuum Mechanics and Thermodynamics 1 Computational Optimization and Applications 1 Computational Economics 1 Set-Valued Analysis 1 Numerical Linear Algebra with Applications 1 Russian Journal of Numerical Analysis and Mathematical Modelling 1 Advances in Computational Mathematics 1 Discrete and Continuous Dynamical Systems 1 Computing and Visualization in Science 1 Vietnam Journal of Mathematics 1 Abstract and Applied Analysis 1 Chaos 1 Fractional Calculus & Applied Analysis 1 Mathematical and Computer Modelling of Dynamical Systems 1 Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 European Journal of Mechanics. B. Fluids 1 Natural Resource Modeling 1 Flow, Turbulence and Combustion 1 Regular and Chaotic Dynamics 1 Optimization and Engineering 1 Differential Equations ...and 22 more Serials
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### Cited in 33 Fields

 191 Numerical analysis (65-XX) 77 Biology and other natural sciences (92-XX) 73 Ordinary differential equations (34-XX) 54 Partial differential equations (35-XX) 51 Fluid mechanics (76-XX) 26 Mechanics of deformable solids (74-XX) 23 Dynamical systems and ergodic theory (37-XX) 19 Mechanics of particles and systems (70-XX) 14 Operations research, mathematical programming (90-XX) 14 Systems theory; control (93-XX) 13 Classical thermodynamics, heat transfer (80-XX) 11 Statistical mechanics, structure of matter (82-XX) 9 Probability theory and stochastic processes (60-XX) 8 Statistics (62-XX) 8 Computer science (68-XX) 7 Calculus of variations and optimal control; optimization (49-XX) 7 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 6 Geophysics (86-XX) 4 Integral equations (45-XX) 3 Combinatorics (05-XX) 3 Optics, electromagnetic theory (78-XX) 3 Information and communication theory, circuits (94-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Real functions (26-XX) 2 Quantum theory (81-XX) 1 General and overarching topics; collections (00-XX) 1 History and biography (01-XX) 1 Difference and functional equations (39-XX) 1 Approximations and expansions (41-XX) 1 Functional analysis (46-XX) 1 Operator theory (47-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Mathematics education (97-XX)