The High-Order ADI Difference Method and Extrapolation Method for Solving the Two-Dimensional Nonlinear Parabolic Evolution Equations

Xin Shen, Xuehua Yang and Haixiang Zhang ()
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Xin Shen: School of Science, Hunan University of Technology, Zhuzhou 412007, China
Xuehua Yang: School of Science, Hunan University of Technology, Zhuzhou 412007, China
Haixiang Zhang: School of Science, Hunan University of Technology, Zhuzhou 412007, China

Mathematics, 2024, vol. 12, issue 22, 1-21

Abstract: In this paper, the numerical solution for two-dimensional nonlinear parabolic equations is studied using an alternating-direction implicit (ADI) Crank–Nicolson (CN) difference scheme. Firstly, we use the CN format in the time direction, and then use the CN format in the space direction before discretizing the second-order center difference quotient. In addition, we strictly prove that the proposed ADI difference scheme has unique solvability and is unconditionally stable and convergent. The extrapolation method is further applied to improve the numerical solution accuracy. Finally, two numerical examples are given to verify our theoretical results.

Keywords: nonlinear evolution equation; finite difference method; alternate direction implicit; stability; convergence (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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