An approximate analytic solution of the nonlinear Riccati differential equation. (English) Zbl 1210.34016

Summary: A hybrid method which combines the Adomian decomposition method (ADM), the Laplace transform algorithm and the Padé approximant is introduced to solve the approximate analytic solutions of the nonlinear Riccati differential equations. This hybrid method demonstrates accurate and reliable results, and has a great improvement in the ADM truncated series solution which diverges rapidly as the applicable domain increases. Three examples herein are given to demonstrate a good accuracy and fast convergence in comparison with the exact solution.


34A34 Nonlinear ordinary differential equations and systems
34A45 Theoretical approximation of solutions to ordinary differential equations
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