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Zbl 1210.65131
Mohammadi, F.; Hosseini, M.M.
A comparative study of numerical methods for solving quadratic Riccati differential equations. (English)
[J] J. Franklin Inst. 348, No. 2, 156-164 (2011). ISSN 0016-0032; ISSN 1879-2693/e

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.

MSC 2000:: *65L05 Initial value problems for ODE (numerical methods)
34A34 Nonlinear ODE and systems, general
65T60 Wavelets
65L60 Finite numerical methods for ODE
65L20 Stability of numerical methods for ODE

Keywords: numerical examples; convergence; Legendre wavelet method; quadratic Riccati differential equations

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