A Matched Alternating Direction Implicit (ADI) Method for Solving the Heat Equation with Interfaces

A Matched Alternating Direction Implicit (ADI) Method for Solving the Heat Equation with Interfaces

A novel Douglas alternating direction implicit (ADI) method is proposed in this work to solve a two-dimensional (2D) heat equation with interfaces. The ADI scheme is a powerful finite difference method for solving parabolic equations, due to its unconditional stability and high efficiency. However, it suffers from a serious accuracy reduction in space for interface problems with different mater...

Solving Two-Dimensional Fuzzy Partial Dierential Equation by the Alternating Direction Implicit Method

solving two-dimensional fuzzy partial dierential equation by the alternating direction implicit method

High-accuracy alternating segment explicit-implicit method for the fourth-order heat equation

Based on a group of new Saul’yev type asymmetric difference schemes constructed by author, a high-order, unconditionally stable and parallel alternating segment explicit-implicit method for the numerical solution of the fourth-order heat equation is derived in this paper. The truncation error is fourth-order in space, which is much more accurate than the known alternating segment explicit-impli...

solving two-dimensional fuzzy partial dierential equation by the alternating direction implicit method

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