基于有限差分法的二维边值问题的数值分析

  1. 在matlab中分析基于分离变量法的解析解； 2. 利用简单迭代法求解，与解析法结论对比，分析求解结果的精确度。分析过程至少包括：在网格尺寸为0.1 m和1 m两种条件下，两次迭代差值最大为10-10时的分析结论； 3. 利用超松弛迭代法分析，选择松弛因子，分析其对收敛速度（即迭代次数）的影响，并确定最优值。分析过程至少包括：在网格尺寸为0.1和1两种条件下，两次迭代差值最大为10-10时，迭代次数随松弛因子的变化，得到对应的最优松弛因子，与经验值（课本165页式子3.7.15）进行对比。(1. Analyze the analytical solution based on the separation variable method in matlab. 2. Using a simple iterative method to solve, compared with the results of the analytical method to analyze the accuracy of the solution. The analysis process at least includes the following conclusions: when the mesh size is 0.1m and 1m, the maximum difference between two iterations is 10-10. 3. Analyze using the relaxation relaxation iteration method, select the relaxation factor, analyze its influence on the convergence speed (ie the number of iterations), and determine the optimal value. The analysis process at least includes the following: when the mesh size is 0.1 and 1 and the maximum difference between two iterations is 10-10, the number of iterations varies with the relaxation factor, and the corresponding optimal relaxation factor and empirical value are obtained ( Textbook 165 pages (3.7.15) for comparison.)

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