Maximum error estimates of two linearized compact difference schemes for two-dimensional nonlinear Sobolev equations
The authors consider two types of two-dimensional nonlinear Sobolev equations and their numerical solutions obtained using two classes of higher-order numerical schemes on the time discretizations, and compact difference operator in spatial dimension. The main contribution of this paper is the proof the convergence in maximum norm for the compact difference scheme from [\textit{X. Chen} et al., Numer. Methods Partial Differ. Equations 34, No. 3, 1093--1112 (2018; Zbl 1407.65098)], as well as a new and more efficient three-level linearized compact difference scheme for solving the equations. The essential improvement for the three-level linearized compact difference scheme is that the coefficient matrix is fixed which costs much less CPU time then in the case of two-level scheme. The numerical tests which confirm the theoretical results and demonstrate the efficiency of both difference schemes are given.
scientific article; zbMATH DE number 7630333
scientific article