An efficient method for quadratic Riccati differential equation. (English) Zbl 1221.65193

Aminikhah, Hossein; Hemmatnezhad, Milad

Commun. Nonlinear Sci. Numer. Simul. 15, No. 4, 835-839 (2010).

Summary: A new form of homotopy perturbation method (NHPM) has been adopted for solving the quadratic Riccati differential equation. In this technique, the solution is considered as a Taylor series expansion converges rapidly to the exact solution of the nonlinear equation. Having found the exact solution of the Riccati equation, the capability and the simplicity of the proposed technique is clarified.

MSC:

65L99	Numerical methods for ordinary differential equations
34A45	Theoretical approximation of solutions to ordinary differential equations

Keywords:

NHPM; nonlinear equations; Riccati equation; Taylor series expansion

References:

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