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Original Articles

Legendre spectral method for solving integral and integro-differential equations

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Pages 187-203 | Received 18 Mar 1999, Published online: 20 Mar 2007
 

Abstract

A new spectral approximation of an integral based on Legendre approximation at the zeros of the first term of the residual is presented. The method is used to solve integral and integro-differential equations. The method generates approximations to the lower order derivatives of the function through successive integrations of the Legendre polynomial approximation to the highest order derivative. Numerical results are included to confirm the efficiency and accuracy of the method.

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