Efficient Legendre pseudospectral method for solving integral and integro-differential equations

This paper introduces a new approach to obtain the integration matrices using Legendre power expansion Pn(x)Pn(x). This method generates approximations to the lower order derivatives of the function through successive integrations of the Legendre polynomials to the highest order derivatives. This method is used to solve integral and integro-differential equations. The advantages of the suggested integration matrices emerged through comparisons with other ones.