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Arenas, Abraham J.; González-Parra, Gilberto; Jódar, Lucas; Villanueva, Rafael-J.

Piecewise finite series solution of nonlinear initial value differential problem. (English) Zbl 1166.65350

Appl. Math. Comput. 212, No. 1, 209-215 (2009).
Summary: We apply a piecewise finite series as a hybrid analytical-numerical technique for solving some systems of nonlinear ordinary differential equations (ODEs). The finite series is generated by using the Adomian decomposition method, which is an analytical method that gives the solution based on a power series and has been successfully used in a wide range of problems in applied mathematics.
We study the influence of the step size and the truncation order of the piecewise finite series Adomian (PFSA) method on the accuracy of the solutions when applied to nonlinear ODEs. Numerical comparisons between the PFSA method with different time steps and truncation orders against Runge-Kutta type methods are presented. Based on the numerical results we propose a low value truncation order approach with small time step size. The numerical results show that the PFSA method is accurate and easy to implement with the proposed approach.

Cited in 8 Documents

MSC:

65L05 Numerical methods for initial value problems involving ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems
65L50 Mesh generation, refinement, and adaptive methods for ordinary differential equations
65L70 Error bounds for numerical methods for ordinary differential equations
65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations

Keywords:

piecewise finite series; convergence; Lotka-Volterra system; Riccati equation; Adomian decomposition method; step size; truncation order; Runge-Kutta type methods; numerical results; power series
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\textit{A. J. Arenas} et al., Appl. Math. Comput. 212, No. 1, 209--215 (2009; Zbl 1166.65350)
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