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A comparative study of numerical methods for solving quadratic Riccati differential equations. (English) Zbl 1210.65131
Summary: We use a Legendre wavelet method for solving quadratic Riccati differential equations and perform a comparative study between the proposed method and other existing methods. Our results show that in comparison with other existing methods, the Legendre wavelet method provides a fast convergent series of easily computable components. The present study is illustrated by exploring two kinds of nonlinear Riccati differential equations that shows the pertinent features of the Legendre wavelet method.

65L05Initial value problems for ODE (numerical methods)
34A34Nonlinear ODE and systems, general
65T60Wavelets (numerical methods)
65L60Finite elements, Rayleigh-Ritz, Galerkin and collocation methods for ODE
65L20Stability and convergence of numerical methods for ODE
Full Text: DOI
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