Novel numerical methods for second order partial Volterra integro-differential equations in two dimensional space
摘要
A spectral method in conjunction with the variable two-step backward differentiation formula (BDF2) is formulated for solving two-dimensional Volterra integro-differential equations with partial derivatives up to second order. Firstly we transform the supplementary conditions into equivalent equations, then some functional and variable transformations are adopted to change the equations into another second order partial integro-differential equations. Before we carry out spectral discretization, we discretize the first order derivative relating to the second variable by BDF2. Thereafter the spectral error analysis procedure is described to estimate the error about the first variable in