微分方程数值解课程设计

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1、利用五点差分格式求解拉普拉斯方程的混合边值问题要求：给出问题，计算格式，格式的矩阵形式，线性代数方程组求解的数值方法，稳定性，格式的截断误差；程序流程图；沿y=1画出计算结果与精确解的比较图形以及误差图形(在一个图上)；分析两个迭代法的收敛速度。E=-1.10000.5000000000000.5000-2.10000.5000000000000.5000-2.10000.5000000000000.5000-2.10000.5000000000000.5000-2.10000.5000000000000.5000-2.10000.500

2、0000000000.5000-2.10000.5000000000000.5000-2.10000.5000000000000.5000-2.10000.5000000000000.5000-2.1000h=0.1Em=-2.10001.0000000000001.0000-4.00001.0000000000001.0000-4.00001.0000000000001.0000-4.00001.0000000000001.0000-4.00001.0000000000001.0000-4.00001.0000000000001.000

3、0-4.00001.0000000000001.0000-4.00001.0000000000001.0000-4.00001.0000000000001.0000-4.0000K=0.500000000000001.000000000000001.000000000000001.000000000000001.000000000000001.000000000000001.000000000000001.000000000000001.000000000000001.0000A=[EKzeros(10)zeros(10)zeros(10

4、)zeros(10)zeros(10)zeros(10)zeros(10)zeros(10)KEmKzeros(10)zeros(10)zeros(10)zeros(10)zeros(10)zeros(10)zeros(10)zeros(10)KEmKzeros(10)zeros(10)zeros(10)zeros(10)zeros(10)zeros(10)zeros(10)zeros(10)KEmKzeros(10)zeros(10)zeros(10)zeros(10)zeros(10)zeros(10)zeros(10)zeros(1

5、0)KEmKzeros(10)zeros(10)zeros(10)zeros(10)zeros(10)zeros(10)zeros(10)zeros(10)KEmKzeros(10)zeros(10)zeros(10)zeros(10)zeros(10)zeros(10)zeros(10)zeros(10)KEmKzeros(10)zeros(10)zeros(10)zeros(10)zeros(10)zeros(10)zeros(10)zeros(10)KEmKzeros(10)zeros(10)zeros(10)zeros(10)ze

6、ros(10)zeros(10)zeros(10)zeros(10)KEmKzeros(10)zeros(10)zeros(10)zeros(10)zeros(10)zeros(10)zeros(10)zeros(10)KEm]g=0-0.0100-0.0400-0.0900-0.1600-0.2500-0.3600-0.4900-0.6400-0.81000.010000000000-9.90000.040000000000-9.60000.090000000000-9.10000.160000000000-8.40000.250000

7、000000-7.50000.360000000000-6.40000.490000000000-5.10000.640000000000-3.60005.81009.90009.60009.10008.40007.50006.40005.10003.60001.9000U=zeros(100，1)nm=100;w=10^-2;jacobi(A,h*g,U,nm,w)迭代次数为n=44方程组的解为x=00.00870.03500.07950.14370.22900.33680.46800.62280.8006-0.008700.02600

8、.07020.13380.21870.32610.45720.61210.7902-0.0350-0.026000.04390.10720.19150.29840.42890.58320.76