关键词: 抛物型方程, 高精度差分格式, 截断误差

Abstract: Parabolic partial differential equations play an important role in the fields of engineering technology and natural science, especially in the fields of seepage, heat conduction and diffusion. This paper mainly studies the numerical solution of parabolic equations. On the basis of mesh segmentation. First, a differential format with parameters is given. The Taylor series expansion method and the undetermined coefficient method are used to make the truncation error of the difference format reach O(τ^3+h^5). The parameters are determined by the equations to obtain a two⁃layer high⁃precision difference format. Then the Fourier analysis method is used. Solve the condition that achieves stability under this precision, that is r≤(19+√(1 141))/60.The numerical solution is compared with the exact solution by numerical examples, which verifies that the new method is feasible and effective.

Key words: Parabolic equation, High precision differential format, Truncation errors