How to use adomian decomposition method for solving odes?

Randolph Rach

You may also be interested in some of my other publications:

A bibliography of the theory and applications of the Adomian decomposition method, 1961-2011

R. Rach

Kybernetes, Volume 41, Issues 7/8, 2012, Pages 1087-1148

Select Supplemental Bibliography of the Adomian Decomposition Method - Post-2011.pdf

A new modified Adomian decomposition method for higher-order nonlinear dynamical systems

J.-S. Duan, R. Rach, A.-M. Wazwaz

CMES: Computer Modeling in Engineering & Sciences, Vol. 94, No. 1, 2013, Pp. 77-118.

24. Solution of higher-order, multipoint, nonlinear boundary value problems with high-order Robin-type boundary conditions by the Adomian decomposition method

R. Rach, J.-S. Duan, A.-M. Wazwaz

Applied Mathematics and Information Sciences, Vol. 10, No. 4, 2016, Pp. 1231-1242.

23. Higher-order numeric solutions of the Lane-Emden type equations derived from the multi-stage modified decomposition method

J.-S. Duan, R. Rach, A.-M. Wazwaz

International Journal of Computer Mathematics, International Journal of Computer Mathematics, Volume 94, No. 1, 2017, 197-215.

22. The degenerate form of the Adomian polynomials in the power series method for nonlinear ordinary differential equations

J.-S. Duan, R. Rach

Journal of Mathematics and System Science, Volume 5, Pages 411-428, 2015.

21. On the solution of non-isothermal reaction-diffusion model equations in a spherical catalyst by the modified Adomian method

R. Rach, J.-S. Duan, A.-M. Wazwaz

Chemical Engineering Communications, Volume 202, Issue 8, 2015, Pages 1081-1088.

20. A new parametric algorithm for isothermal flash calculations by the Adomian decomposition of Michaelis-Menten type nonlinearities

H. Fatoorehchi, H. Abolghasemi, R. Rach

Fluid Phase Equilibria, Vol. 395, 2015, Pp. 44-50.

19. Steady-state concentrations of carbon dioxide absorbed into phenyl glycidyl ether solutions by the Adomian decomposition method

J.-S. Duan, R. Rach, A.-M. Wazwaz

Journal of Mathematical Chemistry, Vol. 53, 2015, Pages 1054-1067.

18. A reliable algorithm for positive solutions of nonlinear boundary value problems by the multistage Adomian decomposition method,

J.-S. Duan, R. Rach, A.-M. Wazwaz,

Open Engineering, Volume 5, Issue 1, 59-74, 2014, DOI: 10.1515/eng-2015-0007.

17. The Volterra integral form of the Lane-Emden equation: New derivations and solution by the Adomian decomposition method

R. Rach, A.M. Wazwaz and J.S. Duan

Journal of Applied Mathematics and Computing, Volume 47, Issue 1, 2015, Pages 365-379.

16. A reliable analysis of oxygen diffusion in a spherical cell with nonlinear oxygen uptake kinetics

R. Rach, A.-M. Wazwaz, J.-S. Duan

International Journal of Biomathematics, Vol. 07, No. 02, March 2014, 1450020 (2014) [12 pages].

15. Solving coupled Lane-Emden boundary value problems in catalytic diffusion reactions by the Adomian decomposition method

R. Rach, J.-S. Duan, A.-M. Wazwaz

Journal of Mathematical Chemistry, Volume 52, Issue 1, 2014, Pages 255-267.

14. A study on the systems of the Volterra integral forms of the Lane-Emden equations by the Adomian decomposition method

A.-M. Wazwaz, R. Rach, J.-S. Duan

Mathematical Methods in the Applied Sciences, Vol. 37, Issue 1, 2014, Pages 10-19.

13. A new modified Adomian decomposition method for higher-order nonlinear dynamical systems

J.-S. Duan, R. Rach, A.-M. Wazwaz

CMES: Computer Modeling in Engineering & Sciences, Vol. 94, No. 1, 2013, Pp. 77-118.

12. A new modified Adomian decomposition method and its multistage form for solving nonlinear boundary value problems with Robin boundary conditions

J.-S. Duan, R. Rach, A.-M. Wazwaz, T. Chaolu, Z. Wang

Applied Mathematical Modelling, Vol. 37, Nos. 20/21, 2013, Pages 8687-8708.

11. The Adomian decomposition method with convergence acceleration techniques for nonlinear fractional differential equations

J.-S. Duan, T. Chaolu, R. Rach, L. Lu

Computers and Mathematics with Applications, Volume 66, Issue 5, 2013, pp. 728-736.

10. On the effective region of convergence of the decomposition series solution

J.-S. Duan, R. Rach, Z. Wang

Journal of Algorithms and Computational Technology, Volume 7, 2013, Pages 227-247.

9. A bibliography of the theory and applications of the Adomian decomposition method, 1961-2011

R. Rach

Kybernetes, Volume 41, Issues 7/8, 2012, Pages 1087-1148.

8. Adomian decomposition method for solving the Volterra integral form of the Lane-Emden equations with initial values and boundary conditions

A.-M. Wazwaz, R. Rach, J.-S. Duan

Applied Mathematics and Computation, Volume 219, Issue 10, 2013 Pages 5004-5019.

7. A review of the Adomian decomposition method and its applications to fractional differential equations

J.-S. Duan, R. Rach, D. Baleanu, A.-M. Wazwaz

Communications in Fractional Calculus, Volume 3, Issue 2, 2012, Pages 73-99.

6. A reliable modification of the Adomian decomposition method for higher-order nonlinear differential equations

R. Rach, A.-M. Wazwaz, J.-S. Duan

Kybernetes, Volume 42, Issues 1/2, 2013, Pages 282-308.

5. Solution of the model of beam-type micro- and nano-scale electrostatic actuators by a new modified Adomian decomposition method for nonlinear boundary value problems

J.-S. Duan, R. Rach, A.-M. Wazwaz

International Journal of Non-Linear Mechanics, Volume 49, 2013, Pages 159-169.

4. Higher-order numeric Wazwaz-El-Sayed modified Adomian decomposition algorithms

J.-S. Duan, R. Rach

Computers and Mathematics with Applications, Volume 63, Issue 11, 2012, Pages 1557-1568.

3. Solutions of the initial value problem for nonlinear fractional ordinary differential equations by the Rach-Adomian-Meyers modified decomposition method

J.-S. Duan, T. Chaolu, R. Rach

Applied Mathematics and Computation, Volume 218, Issue 17, 2012, Pages 8370-8392.

2. A new modification of the Adomian decomposition method for solving boundary value problems for higher order differential equations

J.-S. Duan, R. Rach

Applied Mathematics and Computation, Volume 218, Issue 8, 2011, Pages 4090-4118.

1. New higher-order numerical one-step methods based on the Adomian and the modified decomposition methods

J.-S. Duan, R. Rach

Applied Mathematics and Computation, Volume 218, Issue 6, 2011, Pages 2810-2828.

See also papers by Jun-Sheng Duan on automated generation of the Adomian polynomials!

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