BVPh swMATH ID: 6575 Software Authors: Liao, Shijun Description: Homotopy analysis method in nonlinear differential equations. ”Homotopy Analysis Method in Nonlinear Differential Equations” presents the latest developments and applications of the analytic approximation method for highly nonlinear problems, namely the homotopy analysis method (HAM). Unlike perturbation methods, the HAM has nothing to do with small/large physical parameters. In addition, it provides great freedom to choose the equation-type of linear sub-problems and the base functions of a solution. Above all, it provides a convenient way to guarantee the convergence of a solution. This book consists of three parts. Part I provides its basic ideas and theoretical development. Part II presents the HAM-based Mathematica package BVPh 1.0 for nonlinear boundary-value problems and its applications. Part III shows the validity of the HAM for nonlinear PDEs, such as the American put option and resonance criterion of nonlinear travelling waves. New solutions to a number of nonlinear problems are presented, illustrating the originality of the HAM. Mathematica codes are freely available online to make it easy for readers to understand and use the HAM. This book is suitable for researchers and postgraduates in applied mathematics, physics, nonlinear mechanics, finance and engineering. Homepage: http://numericaltank.sjtu.edu.cn/BVPh.htm Dependencies: Mathematica Keywords: HAM; Homotopy Analysis Method; Nonlinear Differential Equations Related Software: Matlab; Mathematica; bvp4c; Differentiation Matrix Suite; Adam; NewtonLib; minpack; RODAS; HOMPACK90; FODE; ode45; WKPtest; bvp5c; L-BFGS; AlexNet; DGM; hp-VPINNs; PPINN; DeepXDE; PDE-Net Cited in: 251 Documents Standard Articles 1 Publication describing the Software, including 1 Publication in zbMATH Year Homotopy analysis method in nonlinear differential equations. Zbl 1253.35001Liao, Shijun 2012 all top 5 Cited by 398 Authors 24 Liao, Shijun 23 Hayat, Tasawar 16 Al-saedi, Ahmed Eid Salem 15 Xu, Hang 11 van Gorder, Robert Ashton 7 Vajravelu, Kuppalapalle 7 Wang, Ping 6 Băleanu, Dumitru I. 5 Gómez-Aguilar, José Francisco 5 Muhammad, Taseer 5 Yépez-Martínez, Huitzilin 4 Abbasbandy, Saeid 4 Baxter, Mathew 4 Dewasurendra, Mangalagama 4 Islam, Saeed 4 Kumbhakar, Manotosh 4 Lin, Zhiliang 4 Liu, Zeng 4 Mallory, Kristina 4 Nave, Ophir 4 Pop, Ioan 4 Shehzad, Sabir Ali 4 Xu, Dali 4 Zhao, Yinlong 3 Abbas, Zaheer 3 Asghar, Saleem 3 Cui, Jifeng 3 Escobar-Jiménez, Ricardo Fabricio 3 Hetmaniok, Edyta 3 Khan, Sami Ullah 3 Liang, Songxin 3 Lu, Dongqiang 3 Noorani, Mohd Salmi Mohd 3 Olivares-Peregrino, Victor Hugo 3 Słota, Damian 3 Yang, Zhaochen 3 Zhao, Qingkai 2 Ahmad, Iftikhar 2 Ali, Nasir 2 Alomari, Abedel-Karrem 2 Ashraf, M. Bilal 2 Aziz, Samaira 2 Balamuralitharan, Sundarappan 2 Berx, Jonas 2 Chen, Qingbo 2 Dawar, Abdullah 2 Elbaz, Miriam 2 Faghidian, S. Ali 2 Fiza, Mehreen 2 Ghoreishi, Mohammad 2 Ghoshal, Koeli 2 Golbabai, Ahmad 2 Hashim, Ishak 2 Hendi, Awatif A. 2 Hussain, Syed Tayyab 2 Imtiaz, Maria 2 Indekeu, Joseph O. 2 Khan, Hassan Ali 2 Khan, Masood 2 Khan, Muhammad Ijaz 2 Khan, Noor Saeed 2 Khoshrouye Ghiasi, Emran 2 Kumar Mishra, Hradyesh 2 Kumar, Devendra 2 Kurulay, Muhammet 2 Liu, Jincun 2 Lone, Showkat Ahmad 2 Luo, Xinlong 2 Madhusudhan, R. M. 2 Mahomed, Fazal M. 2 Masjedi, Pedram Khaneh 2 Mastroberardino, Antonio 2 Mohammadyari, Reza 2 Mustafa, Meraj 2 Nagarajaiah, Satish 2 Narayana, Mahesha 2 Nazar, Roslinda Mohd 2 Noeiaghdam, Samad 2 Pandey, Rishi Kumar 2 Raees, Ammarah 2 Rahimi-Esbo, Mazaher 2 Rahimi, J. 2 Rahimipetroudi, Iman 2 Rana, Puneet 2 Reyes, Juan Manuel 2 Saha Ray, Santanu 2 Sahoo, Subhadarshan 2 Sajid, Muhammad 2 Saleh, Reza 2 Sayevand, Khosro 2 Shafiq, Anum 2 Shah, Rasool 2 Shah, Zahir 2 Shahzad, Azeem 2 Shukla, Nisha 2 Siddheshwar, Pradeep G. 2 Singh, Jagdev 2 Singh, Randhir 2 Singh, Vijay P. 2 Sosa, Ivan O. ...and 298 more Authors all top 5 Cited in 87 Serials 20 Numerical Algorithms 13 Applied Mathematical Modelling 13 AMM. Applied Mathematics and Mechanics. (English Edition) 12 Communications in Nonlinear Science and Numerical Simulation 10 Mathematical Problems in Engineering 9 Applied Mathematics and Computation 9 Advances in Difference Equations 8 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 6 Abstract and Applied Analysis 6 Advances in Applied Mathematics and Mechanics 6 International Journal of Applied and Computational Mathematics 5 Chaos, Solitons and Fractals 5 Journal of Computational and Applied Mathematics 5 Mathematics and Computers in Simulation 4 Journal of Fluid Mechanics 4 Wave Motion 4 Applied Mathematics and Mechanics. (English Edition) 4 Computational and Applied Mathematics 4 Chinese Journal of Physics (Taipei) 3 Mathematical Methods in the Applied Sciences 3 International Journal of Numerical Methods for Heat & Fluid Flow 3 European Journal of Mechanics. B. Fluids 3 Journal of Applied Mathematics 3 Advances in Mathematical Physics 2 International Journal of Modern Physics B 2 Acta Mechanica 2 Computers & Mathematics with Applications 2 Computer Physics Communications 2 International Journal of Heat and Mass Transfer 2 Physics Letters. A 2 Numerical Methods for Partial Differential Equations 2 Applied Mathematics Letters 2 Computational Mathematics and Mathematical Physics 2 Filomat 2 Journal of Mathematical Chemistry 2 Nonlinear Dynamics 2 Journal of Applied Mechanics and Technical Physics 2 International Journal of Nonlinear Sciences and Numerical Simulation 2 Boletim da Sociedade Paranaense de Matemática. Terceira Série 2 Journal of Physics A: Mathematical and Theoretical 2 S\(\vec{\text{e}}\)MA Journal 2 Mathematical Sciences 2 Journal of Mathematics 1 Computers and Fluids 1 Computer Methods in Applied Mechanics and Engineering 1 Journal of Computational Physics 1 Journal of Mathematical Analysis and Applications 1 Journal of Mathematical Physics 1 Physica A 1 Demonstratio Mathematica 1 The Journal of the Indian Mathematical Society. New Series 1 Studies in Applied Mathematics 1 Acta Applicandae Mathematicae 1 Journal of the Nigerian Mathematical Society 1 Acta Mathematicae Applicatae Sinica. English Series 1 Journal of Symbolic Computation 1 Mathematical and Computer Modelling 1 Journal of Scientific Computing 1 International Journal of Computer Mathematics 1 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 1 Advances in Computational Mathematics 1 Complexity 1 Differential Equations and Dynamical Systems 1 Chaos 1 New Journal of Physics 1 European Journal of Mechanics. A. Solids 1 Nonlinear Analysis. Real World Applications 1 Mathematical Modelling and Analysis 1 Proceedings of the National Academy of Sciences, India. Section A. Physical Sciences 1 Journal of Applied Mathematics and Computing 1 Thai Journal of Mathematics 1 Boundary Value Problems 1 Inverse Problems in Science and Engineering 1 Differential Equations & Nonlinear Mechanics 1 Acta Mechanica Sinica 1 Journal of Biological Dynamics 1 International Journal of Biomathematics 1 Journal of Nonlinear Science and Applications 1 Differential Equations and Applications 1 Bulletin of Mathematical Analysis and Applications 1 Symmetry 1 International Journal of Structural Stability and Dynamics 1 Arabian Journal for Science and Engineering 1 Numerical Algebra, Control and Optimization 1 Applied Mathematics and Nonlinear Sciences 1 Journal of Computational and Theoretical Transport 1 Russian Journal of Nonlinear Dynamics all top 5 Cited in 26 Fields 107 Fluid mechanics (76-XX) 90 Numerical analysis (65-XX) 81 Partial differential equations (35-XX) 46 Ordinary differential equations (34-XX) 38 Classical thermodynamics, heat transfer (80-XX) 24 Mechanics of deformable solids (74-XX) 14 Biology and other natural sciences (92-XX) 12 Real functions (26-XX) 8 Statistical mechanics, structure of matter (82-XX) 6 Integral equations (45-XX) 4 Dynamical systems and ergodic theory (37-XX) 4 Calculus of variations and optimal control; optimization (49-XX) 4 Probability theory and stochastic processes (60-XX) 3 Integral transforms, operational calculus (44-XX) 3 Computer science (68-XX) 3 Mechanics of particles and systems (70-XX) 3 Systems theory; control (93-XX) 3 Information and communication theory, circuits (94-XX) 2 Approximations and expansions (41-XX) 2 Quantum theory (81-XX) 2 Geophysics (86-XX) 1 Algebraic geometry (14-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Special functions (33-XX) 1 Operations research, mathematical programming (90-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) Citations by Year