A Legendre spectral method for multidimensional partial Volterra integro-differential equations

Abstract

We present a Legendre spectral method for solving multidimensional partial Volterra integro-differential equations. The main idea of our approach is first to employ some function transformations and variable transformations to transform the equations into new partial Volterra integro-differential equations, and then the Legendre spectral method is used to solve the equivalent equations. We derive error bounds in L∞- and L2-norms, which indicate that the errors of solution and the first order partial derivative decay exponentially. Three numerical examples are displayed to confirm the reliability of the Legendre spectral analysis.