SOLUTION OF HIGHER ORDER VOLTERRA
INTEGRO-DIFFERENTIAL EQUATIONS
BY LEGENDRE WAVELETS
Raghvendra S. Chandel$^1$, Amardeep Singh$^2$, Devendra Chouhan$^3$
$^1$Department of Mathematics
Govt. Geetanjali Girls College
Bhopal, INDIA
$^2$Department of Mathematics
Govt. MVM College
Bhopal, INDIA
$^3$Department of Mathematics
IES, IPS Academy
Indore, INDIA
Abstract. In this paper the solution of higher order Volterra integro-differential equations using Legendre wavelets is presented. The problem is reduced into the solution of non-linear algebraic equations using Legendre wavelets. A reliable approach is also discussed for the convergence of the Legendre wavelets. To demonstrate the validity and applicability of the proposed method, some examples have been discussed. The results in these examples demonstrate the reliability and efficiency of the proposed method. The results obtained by the Legendre wavelet method are very near to exact solution.
AMS Subject classification: 42C40, 42C10, 45J05
Keywords and phrases: Legendre wavelets, Legendre polynomials, Legendre wavelet method, Gaussian integration, integro-differential equations


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DOI: 10.12732/ijam.v28i4.6

Volume: 28
Issue: 4
Year: 2015