Iterative Methods For The Forward-Backward Heat Equation
Xiao-liang Cheng 1, Jie Sun 21 Department of Mathematics, Zhejiang University, Hangzhou 310028, China
2 Department of Mathematics, Zhejiang University, Hangzhou 310028, China; and Department of Mathematics, Zhejiang University of Finance and Economics, Hangzhou 310012, China
In this paper we propose the finite difference method for the forward-backward heat equation. We use a coarse-mesh second-order central difference scheme at the middle line mesh points and derive the error estimate. Then we discuss the iterative method based on the domain decomposition for our scheme and derive the bounds for the rates of convergence. Finally we present some numerical experiments to support our analysis.
Key words: Forward-backward heat equation; Finite difference method; Iterative method; Coarse mesh.