A High-Precision Compact Locally One-Dimensional Conservative Spline Scheme for a Two-Dimensional Diffusion Equation in a Quasi-linear Formulation

This article presents a method of numerical integration of a mixed initial-boundary value problem for two-dimensional second-order parabolic quasilinear diffusion equation with quasilinear diffusion coefficient and linear external source, that provides a 4th order spatial approximation. We consider an algorithm for constructing the operators of a difference scheme on a compact template using sequential coordinate-wise application of spline inter-polation. The theoretical calculation of the approximation order provided by the considered difference scheme is given, and the condition under which the scheme is stable is found. The results of computational experiments confirming the theoretically found value for the approx-imation order are presented.