A CLASS OF HIGH ACCURACY EXPLICIT DIFFERENCE SCHEMES FOR SOLVING THREE-DIMENSIONAL PARABOLIC EQUATIONS

Abstract

A class of explicit difference schemes with high accuracy for solving three-dimensional parabolic equations are given.  First, a difference approximation expression of \(\frac{ϑu}{ϑt}\) is deduced at a special node (x_j, y_k, z_l, t_n+1); a class of explicit difference schemes are constructed by the method of undetermined coefficients, and appropriate parameters are chosen to endow the truncation error of schemes is O (∆t³ + ∆x⁴).  In turn, the new di®erence schemes are proved to be stable if r < \(\frac{1}{4}\) with the Fourier analysis method.  Finally, the numerical experiment shows the numerical solutions of difference schemes and the exact solutions are matched and the difference schemes are effective.