A high-order accuracy explicit difference scheme with branching stability for solving four-dimensional parabolic equations

作者：Zhan, Yongqiang^*

来源：Italian Journal of Pure and Applied Mathematics, 2018, (39): 672-682.

• Explicit difference schemes
• Fourier analysis methods
• High-order accuracy
• Method of undetermined coefficients
• Numerical experiments
• Numerical solution
• Parabolic Equations
• Truncation errors

A high-order explicit difference scheme for solving four-dimensional parabolic equations is given. The scheme is constructed by the method of undetermined coefficients, and appropriate parameter is chosen to endow the truncation error of schemes is O (Δt4+ Δx4). And the new difference scheme is proved to be stable if r ≤1/12 with the Fourier analysis method. Finally, the numerical experiment shows the numerical solutions of difference scheme and the exact solutions are matched and the difference scheme is effective.

• 出版日期2018-2