THE EXTENDED LEGENDRE WAVELETS OPERATIONAL MATRIX OF INTEGRATION AND ITS APPLICATIONS

THE EXTENDED LEGENDRE WAVELETS OPERATIONAL MATRIX OF INTEGRATION AND ITS APPLICATIONS

V. K. Sharma, S. Singh, H. M. Srivastava

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Abstract

In this paper, the general operational matrix of integration P based on the extended Legendre wavelets has been developed which generalizes the idea of the operational matrix of integration for μ = 2 given in [30]. A brief procedure for forming this matrix has been discussed. Also, we have solved Bessel differential equation of order zero by using extended Legendre wavelets method for different values of μ, M and k. The results show the better accuracy of the proposed method, which is justified through the illustrative examples.

Keywords

Extended Legendre wavelet, operational matrix of integration, Legendre polynomials, orthonormal set.