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