C 代码 应用 的 p 方法版本 有限元法 （FEM） 到线性 一维中的两点边界值问题 （BVP）.rar

19 January 2020 11:30:35 AM FEM1D_PMETHOD C version Solve the two-point boundary value problem - d/dX (P dU/dX) + Q U = F on the interval [-1,1], with U(-1) = U(1) = 0. The P method is used, which represents U as a weighted sum of orthogonal polynomials. Highest degree polynomial to use is 2 Number of points to be used for output = 10 Problem #2: U=cos(0.5*pi*x), P=1, Q=0, F=0.25*pi*pi*cos(0.5*pi*x) Basis function orthogonality test: i j b(i,j)/a(i) 0 0 1 0 1 2.08167e-17 0 2 -8.32667e-17 1 0 3.46945e-17 1 1 1 1 2 1.73472e-17 2 0 -3.90313e-16 2 1 4.87891e-17 2 2 1.28571 Representation of solution: Basis function coefficients: 0 0.95493 1 -1.25361e-18 2 -0.283868 X Approximate Solution -1 0 -0.8 0.29881 -0.6 0.582087 -0.4 0.811679 -0.2 0.960335 0 1.0117 0.2 0.960335 0.4 0.811679 0.6 0.582087 0.8 0.29881 1 0 Comparison of computed and exact solutions: X U computed U exact Difference -1 0 6.12323e-17 6.12323e-17 -0.8 0.29881 0.309017 0.0102071 -0.6 0.582087 0.587785 0.0056984 -0.4 0.811679 0.809017 -0.0026619 -0.2 0.960335 0.951057 -0.00927815 0 1.0117 1 -0.0117033 0.2 0.960335 0.951057 -0.00927815 0.4 0.811679 0.809017 -0.0026619 0.6 0.582087 0.587785 0.0056984 0.8 0.29881 0.309017 0.0102071 1 0 6.12323e-17 6.12323e-17 Big L2 error = 0.00779738 FEM1D_PMETHOD Normal end of execution. 19 January 2020 11:30:35 AM