A semi-discrete numerical scheme for nonlocally regularized KdV-type equations

A general class of KdV-type wave equations regularized with a convolution-type nonlocality in space is considered. The differs from the nonlinear nonlocal unidirectional previously studied by addition linear convolution term involving third-order derivative. To solve Cauchy problem we propose semi-discrete numerical method based on uniform spatial discretization, that an extension published work present authors. We prove convergence as mesh size goes to zero. also localization error resulting finite domain significantly less than given threshold if large enough. illustrate theoretical results, some experiments are carried out for Rosenau-KdV equation, Rosenau-BBM-KdV equation and integro-differential equation. conducted three particular choices kernel function confirm estimates provide.