%0 Journal Article %1 Lin2012106 %A Lin, Yezhi %A Liu, Yinping %A Li, Zhibin %D 2012 %J Computer Physics Communications %K ODEs adomain decomposition dynamics method software %N 1 %P 106 - 117 %R 10.1016/j.cpc.2011.08.001 %T Symbolic computation of analytic approximate solutions for nonlinear differential equations with initial conditions %U http://www.sciencedirect.com/science/article/pii/S0010465511002736 %V 183 %X The Adomian decomposition method (ADM) is one of the most effective methods for constructing analytic approximate solutions of nonlinear differential equations. In this paper, based on the new definition of the Adomian polynomials, and the two-step Adomian decomposition method (TSADM) combined with the Padé technique, a new algorithm is proposed to construct accurate analytic approximations of nonlinear differential equations with initial conditions. Furthermore, a MAPLE package is developed, which is user-friendly and efficient. One only needs to input a system, initial conditions and several necessary parameters, then our package will automatically deliver analytic approximate solutions within a few seconds. Several different types of examples are given to illustrate the validity of the package. Our program provides a helpful and easy-to-use tool in science and engineering to deal with initial value problems. Program summary Program title: NAPA Catalogue identifier: AEJZ_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEJZ_v1_0.html Program obtainable from: CPC Program Library, Queenʼs University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 4060 No. of bytes in distributed program, including test data, etc.: 113 498 Distribution format: tar.gz Programming language: MAPLE R13 Computer: PC Operating system: Windows XP/7 RAM: 2 Gbytes Classification: 4.3 Nature of problem: Solve nonlinear differential equations with initial conditions. Solution method: Adomian decomposition method and Padé technique. Running time: Seconds at most in routine uses of the program. Special tasks may take up to some minutes.

@article{Lin2012106, abstract = {The Adomian decomposition method (ADM) is one of the most effective methods for constructing analytic approximate solutions of nonlinear differential equations. In this paper, based on the new definition of the Adomian polynomials, and the two-step Adomian decomposition method (TSADM) combined with the Padé technique, a new algorithm is proposed to construct accurate analytic approximations of nonlinear differential equations with initial conditions. Furthermore, a MAPLE package is developed, which is user-friendly and efficient. One only needs to input a system, initial conditions and several necessary parameters, then our package will automatically deliver analytic approximate solutions within a few seconds. Several different types of examples are given to illustrate the validity of the package. Our program provides a helpful and easy-to-use tool in science and engineering to deal with initial value problems. Program summary Program title: NAPA Catalogue identifier: AEJZ_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEJZ_v1_0.html Program obtainable from: CPC Program Library, Queenʼs University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 4060 No. of bytes in distributed program, including test data, etc.: 113 498 Distribution format: tar.gz Programming language: MAPLE R13 Computer: PC Operating system: Windows XP/7 RAM: 2 Gbytes Classification: 4.3 Nature of problem: Solve nonlinear differential equations with initial conditions. Solution method: Adomian decomposition method and Padé technique. Running time: Seconds at most in routine uses of the program. Special tasks may take up to some minutes.}, added-at = {2011-11-24T14:13:03.000+0100}, author = {Lin, Yezhi and Liu, Yinping and Li, Zhibin}, biburl = {https://www.bibsonomy.org/bibtex/261b530e8b037290400c38359461e888e/drmatusek}, doi = {10.1016/j.cpc.2011.08.001}, interhash = {ca6abf23384efeb66862506199f41411}, intrahash = {61b530e8b037290400c38359461e888e}, issn = {0010-4655}, journal = {Computer Physics Communications}, keywords = {ODEs adomain decomposition dynamics method software}, month = {January}, number = 1, pages = {106 - 117}, timestamp = {2012-09-17T02:33:39.000+0200}, title = {Symbolic computation of analytic approximate solutions for nonlinear differential equations with initial conditions}, url = {http://www.sciencedirect.com/science/article/pii/S0010465511002736}, volume = 183, year = 2012 }