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

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-infinity- and L-2-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. (c) 2023 Elsevier B.V. All rights reserved.