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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; Adam; minpack; NewtonLib; RODAS; HOMPACK90; FODE; DeepXDE; PDE-Net; FPINNs; AlexNet; L-BFGS; DiffSharp; DGM; ImageNet; PINNsNTK; AdaGrad; NACLab
Cited in: 219 Publications

Standard Articles

1 Publication describing the Software, including 1 Publication in zbMATH Year
Homotopy analysis method in nonlinear differential equations. Zbl 1253.35001
Liao, Shijun
2012
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Cited by 333 Authors

21 Hayat, Tasawar
18 Liao, Shijun
14 Al-saedi, Ahmed Eid Salem
14 Xu, Hang
11 van Gorder, Robert Ashton
6 Băleanu, Dumitru I.
6 Vajravelu, Kuppalapalle
5 Gómez-Aguilar, José Francisco
5 Wang, Ping
5 Yépez-Martínez, Huitzilin
4 Abbasbandy, Saeid
4 Baxter, Mathew
4 Lin, Zhiliang
4 Mallory, Kristina
4 Mustafa, Meraj
4 Nave, Ophir
4 Pop, Ioan
4 Shehzad, Sabir Ali
4 Zhao, Yinlong
3 Asghar, Saleem
3 Cui, Jifeng
3 Dewasurendra, Mangalagama
3 Escobar-Jiménez, Ricardo Fabricio
3 Hetmaniok, Edyta
3 Kumbhakar, Manotosh
3 Liang, Songxin
3 Muhammad, Taseer
3 Noorani, Mohd Salmi Mohd
3 Olivares-Peregrino, Victor Hugo
3 Słota, Damian
3 Xu, Dali
3 Yang, Zhaochen
3 Zhao, Qingkai
2 Abbas, Zaheer
2 Ahmad, Iftikhar
2 Ali, Nasir
2 Alomari, Abedel-Karrem
2 Ashraf, M. Bilal
2 Aziz, Samaira
2 Balamuralitharan, Sundarappan
2 Chen, Qing-Bo
2 Elbaz, Miriam
2 Faghidian, S. Ali
2 Ghoreishi, Mohammad
2 Ghoshal, Koeli
2 Golbabai, Ahmad
2 Hashim, Ishak
2 Hendi, Awatif A.
2 Hussain, S. T.
2 Imtiaz, Maria
2 Khan, Hassan Ali
2 Khan, Noor Saeed
2 Khan, Sami Ullah
2 Khoshrouye Ghiasi, Emran
2 Kumar Mishra, Hradyesh
2 Kumar, Devendra
2 Kurulay, Muhammet
2 Liu, Jincun
2 Liu, Zeng
2 Luo, Xinlong
2 Madhusudhan, R.
2 Mahomed, Fazal M.
2 Mastroberardino, Antonio
2 Mohammadyari, Reza
2 Nagarajaiah, Satish
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 Shahzad, Azeem
2 Shukla, Nisha
2 Singh, Jagdev
2 Singh, Randhir
2 Singh, Vijay P.
2 Sosa, Ivan O.
2 Sun, Qiang
2 Tao, Longbin
2 Wang, Anyang
2 Wang, Yongyan
2 Wituła, Roman
2 Wu, Zhiqiang
2 Xiao, Hang
2 Yang, Dan
2 You, Xiangcheng
2 Zhang, Guoqi
2 Zhang, Xinxin
2 Zheng, Liancun
2 Zhu, Jing
...and 233 more Authors
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Cited in 80 Serials

20 Numerical Algorithms
13 AMM. Applied Mathematics and Mechanics. (English Edition)
12 Communications in Nonlinear Science and Numerical Simulation
10 Applied Mathematical Modelling
9 Applied Mathematics and Computation
9 Advances in Difference Equations
8 Mathematical Problems in Engineering
6 Abstract and Applied Analysis
6 International Journal of Applied and Computational Mathematics
5 Journal of Computational and Applied Mathematics
4 Journal of Fluid Mechanics
4 Chaos, Solitons and Fractals
4 Applied Mathematics and Mechanics. (English Edition)
4 Computational and Applied Mathematics
4 Advances in Applied Mathematics and Mechanics
3 Mathematical Methods in the Applied Sciences
3 Mathematics and Computers in Simulation
3 International Journal of Numerical Methods for Heat & Fluid Flow
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 Wave Motion
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 European Journal of Mechanics. B. Fluids
2 International Journal of Nonlinear Sciences and Numerical Simulation
2 Boletim da Sociedade Paranaense de Matemática. Terceira Série
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 Numerical Methods for Partial Differential Equations
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 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 Arabian Journal for Science and Engineering
1 Numerical Algebra, Control and Optimization
1 Journal of Computational and Theoretical Transport

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