Uniform Error Estimates for Difference Approximations to NonLinear Pseudo-Parabolic Partial Differential Equations

Two difference-approximation schemes to a nonlinear pseudo-parabolic equation are developed. Each of these schemes is stable and possesses a unique solution which can be obtained by an iterative procedure. By means of a discrete energy estimate, each approximation is shown to converge in the uniform norm to the exact solution with a determined rate. It has also been found that for a fixed lattice, the solution to each of two difference approximations to a certain parabolic problem can be obtained as the limit of a sequence of difference approximations to a pseudo-parabolic problem.