On the solution of the Riccati equation by the decomposition method. (English) Zbl 0995.65073

Summary: We study an analytic solution and a reliable numerical approximation of the Riccati equation by using the Adomian’s decomposition method. The solution is calculated in the form of a series with easily computable components. The numerical results show the effectiveness of the method for this type of equation. Comparing the methodology with some known techniques shows that the present approach is relatively easy and highly accurate.


65L05 Numerical methods for initial value problems involving ordinary differential equations
65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems
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