三维齐次边界抛物型方程的新型交替方向差分格式

A new alternating direction implicit difference method for three-dimensional parabolic differential equations with homogeneous boundary conditions

本文利用算子分解方法推导出了一种求解三维抛物型方程的新型交替方向差分格式,并把这种格式推广到了紧交替方向差分格式。该格式简化了对过渡层边界的处理,降低了扰动项对计算精度的影响,具有无条件稳定,计算速度快的优点。具体算例表明本文格式计算效果良好。

A new alternating direction implicit （ADI） scheme for solving three-dimensional parabolic differential equations is presented based on the idea of the operator decomposition. The scheme is also extended to high-order compact difference scheme. The scheme reduces the impact of the perturbing terms on the accuracy. It is convenient to compute the boundary values of the intermediates. The scheme has the advantages of unconditional stability and costing less computation times. Numerical examples are presented and the results are very satisfactory.