Numerical Solution of Differential Equations by Using Chebyshev Wavelet Collocation Method

Yıl 2013, Cilt: 10 Sayı: 2, - , 01.11.2013

İbrahim Celik

Öz

In this article, a new method known as the Chebyshev
wavelet collocation method is presented for the solution of second-order linear
ordinary differential equations (ODEs). The method is based on the
approximation of the truncated Chebyshev wavelet series. By using the Chebyshev collocation points, an algebraic equation
system has been obtained and solved. Hence the implicit forms of the
approximate solution of second-order linear ordinary differential equations
have been obtained. This present method has been
applied to the Bessel differential equation of order zero and the Lane–Emden
equation. These calculations demonstrate
that the accuracy of the Chebyshev wavelet collocation method is quite high
even in the case of a small number of grid points. The present method is a very
reliable, simple, fast, computationally efficient, flexible, and convenient
alternative method.

Anahtar Kelimeler

Chebyshev wavelet, collocation, Legendre wavelet, approximate solution

Numerical Solution of Differential Equations by Using Chebyshev Wavelet Collocation Method

Öz

In this article, a new method known as the Chebyshev wavelet collocation method is presented for the solution of second-order linear ordinary differential equations (ODEs). The method is based on the approximation of the truncated Chebyshev wavelet series. By using the Chebyshev collocation points, an algebraic equation system has been obtained and solved. Hence the implicit forms of the approximate solution of second-order linear ordinary differential equations have been obtained. This present method has been applied to the Bessel differential equation of order zero and the Lane–Emden equation. These calculations demonstrate that the accuracy of the Chebyshev wavelet collocation method is quite high even in the case of a small number of grid points. The present method is a very reliable, simple, fast, computationally efficient, flexible, and convenient alternative method.

Anahtar Kelimeler

Chebyshev wavelet, collocation, Legendre wavelet, approximate solution

Kaynakça

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