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Wavelet Solution for Class of Nonlinear Integro-differential Equations


Affiliations
1 Department of Mathematics, School of Humanities and Sciences, SASTRA University, Thanjavur-613401, Tamilnadu, India
 

The aim of this work is to study the Legendre wavelets for the solution of a class of nonlinear Volterra integro-differential equation. The properties of Legendre wavelets together with the Gaussian integration method are used to reduce the problem to the solution of nonlinear algebraic equations. Also a reliable approach for convergence of the Legendre wavelet method when applied to nonlinear Volterra equations is discussed. Illustrative examples have been discussed to demonstrate the validity and applicability of the technique and the results obtained by Legendre wavelet method is very nearest to the exact solution. The results demonstrate reliability and efficiency of the proposed method.

Keywords

Legendre Wavelets, Integro-differential Equations, Gaussian Integration, Legendre Wavelet Method, Convergence Analysis
User

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  • Wavelet Solution for Class of Nonlinear Integro-differential Equations

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Authors

S. G. Venkatesh
Department of Mathematics, School of Humanities and Sciences, SASTRA University, Thanjavur-613401, Tamilnadu, India
S. K. Ayyaswamy
Department of Mathematics, School of Humanities and Sciences, SASTRA University, Thanjavur-613401, Tamilnadu, India
S. Raja Balachandar
Department of Mathematics, School of Humanities and Sciences, SASTRA University, Thanjavur-613401, Tamilnadu, India
K. Kannan
Department of Mathematics, School of Humanities and Sciences, SASTRA University, Thanjavur-613401, Tamilnadu, India

Abstract


The aim of this work is to study the Legendre wavelets for the solution of a class of nonlinear Volterra integro-differential equation. The properties of Legendre wavelets together with the Gaussian integration method are used to reduce the problem to the solution of nonlinear algebraic equations. Also a reliable approach for convergence of the Legendre wavelet method when applied to nonlinear Volterra equations is discussed. Illustrative examples have been discussed to demonstrate the validity and applicability of the technique and the results obtained by Legendre wavelet method is very nearest to the exact solution. The results demonstrate reliability and efficiency of the proposed method.

Keywords


Legendre Wavelets, Integro-differential Equations, Gaussian Integration, Legendre Wavelet Method, Convergence Analysis

References





DOI: https://doi.org/10.17485/ijst%2F2013%2Fv6i6%2F33919