一种求解三维抛物方程的迭代方法

为了高效且高精度地求解三维抛物方程(parabolic equation,PE)，提出了一种求解三维PE的迭代方法.该方法采用有限差分（finite difference,FD）近似方法，保留交替方向隐式（alternating direction implicit, ADI）方法的计算模式.推导了该方法对应的相对误差关系式，在推导过程中考虑计算式分裂项丢失带来的误差影响.对比现有的求解三维PE的ADI方法 (记为ADI-PE)和克兰克·尼科森(Crank-Nicolson)求解方法 (记为CN-PE)，该方法能够提高计算精准度，且可通过迭代达到一定计算精度.该方法保留了ADI的计算高效特性，是一种求解三维PE的高效高精准度的方法.

An iterative method for solving 3D parabolic equation

To solve 3D parabolic equation efficiently (PE) and accurately, an iterative method for solving 3D PE is proposed. In this method, finite difference (FD) approximation is applied. The proposed method retains the character of the alternating-direction-implicit (ADI) method. The numerical error caused by the split term of the proposed method is considered in the process of derivation. The proposed method can improve the calculation accuracy compared to the ADI-PE method and Crank-Nicolson parabolic equation (CN-PE) method. A certain accuracy can be achieved by several times of iteration. This method is efficient and accurate for solving 3D PE.