基于MATLAB的静态场边值问题有限差分法的研究

Study of Finite-Difference Method for the Boundary Value of Static Field Based on MATLAB

有限差分法是求解静态场边值问题的一个非常有效的数值解法,它是将求解区域划分为有限个网格点,用一组差分方程代替原来一组微分方程。该方法求得的是近似解而不是精确解。求解区域内网格划分大小关系着计算的精确度,网格尺寸划分越小,计算精确度越高;反之,精确度越低。本文运用MATLAB语言使得有限差分法求解区域内电势分布的解法变得简单、易行,摆脱了传统方法使用C语言较复杂的缺陷。通过仿真验证了算法和程序的有效性。

The finite - difference method is one of the most powerful numerical techniques for solving the boundary value of static field. The finite - difference method basically divides the solution domain into some finite discrete points, and replaces the original differential equations with a set of difference equations. Of cource,the solution is not an exact solution, but an approximate one. The mesh size of the discretized solution domain is a measure of the accracy of the solution： the smaller the mesh size, the better the accuracy ; the bigger the mesh size, the worse the accuracy. The use of MATLAB facilitates the utilization of the finite - difference method to evaluate the field distribution, overcomes the defects of the traditional method for using C language. The simulation examples show that the algorithm and procedures are correct and effective