Generalization of Chebyshev wavelet collocation method to the rth-order differential equations

Abstract

Chebyshev wavelets operational matrices play an important role for the numeric solution of \textit{r}th order differential equations. In this study, operational matrices of \textit{rth} integration of Chebyshev wavelets are presented and a general procedure of these matrices is  correspondingly given. Disadvantages of Chebyshev wavelets methods is eliminated for \textit{r}th integration of $\Psi (t)$. The proposed method is based on the approximation by the truncated Chebyshev wavelet series. Algebraic equation system has been obtained by using the Chebyshev collocation points and solved. The proposed method has been applied to the three nonlinear boundary value problems using quasilinearization technique. Numerical examples showed the applicability and accuracy.

Keywords

• Chebyshev wavelets,collocation method,nonlinear differential equations,quasilinearization technique

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