A HIGH-ORDER ACCURACY EXPLICIT DIFFERENCE SCHEME WITH BRANCHING STABILITY FOR SOLVING FOUR-DIMENSIONAL PARABOLIC EQUATIONS

Abstract

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 (∆t⁴ + ∆x⁴).  And the new difference scheme is proved to be stable if r ≤ \(\frac{1}{12}\) 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.