A generalized two‐cycle componentwise splitting method for solving three‐dimensional parabolic differential equations with variable coefficients on multilayers

Abstract

Describes a generalized two‐cycle componentwise splitting method for solving three‐dimensional parabolic differential equations with variable coefficients which has been developed based on the idea of the regularized difference scheme. The method is simple, unconditionally stable and well suited for simulating fast transient phenomena and for computations on fine spatial meshes. A numerical procedure that employs the generalized two‐cycle componentwise splitting scheme was developed to solve three‐dimensional parabolic differential equations with variable coefficients on multilayers. In the procedure, the generalized “divide and conquer” method for solving tridiagonal linear systems is applied in order to overcome the problem with the unknown value at the interface between layers. Numerical results show that the procedure is accurate and efficient.