Differential Equations Solutions 130

Differential Equations Solutions 130 - 140 Chapter 23....

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Unformatted text preview: 140 Chapter 23. Solutions: Case Study: Finite Differences and Finite Elements Using coefficient functions a(1) and c(3) with true solution u(1) Infinity norm of the error at the grid points for various methods and numbers of interior grid points M M= 1st order finite difference 2nd order finite difference Linear finite elements Quadratic finite elements 9 1.9405e-03 1.9405e-03 4.3912e-04 2.8745e-05 99 1.9529e-05 1.9529e-05 4.3908e-06 3.5282e-09 999 1.9530e-07 1.9530e-07 4.3906e-08 3.6134e-13 PROBLEM 4 Using coefficient functions a(2) and c(1) with true solution u(1) Infinity norm of the error at the grid points for various methods and numbers of interior grid points M M= 1st order finite difference 2nd order finite difference Linear finite elements Quadratic finite elements 9 1.5788e-02 3.8465e-03 1.3904e-03 1.6287e-04 99 1.8705e-03 3.8751e-05 1.3930e-05 1.9539e-08 999 1.8979e-04 3.8752e-07 1.3930e-07 1.9897e-12 PROBLEM 5 Using coefficient functions a(3) and c(1) with true solution u(1) Infinity norm of the error at the grid points for various methods and numbers of interior grid points M M= 1st order finite difference 2nd order finite difference Linear finite elements Quadratic finite elements 9 1.1858e-02 3.6018e-03 8.3148e-04 1.0981e-04 99 1.4780e-03 3.6454e-05 8.2486e-06 1.6801e-06 999 1.5065e-04 3.6467e-07 1.2200e-06 2.5858e-06 PROBLEM 6 Using coefficient functions a(1) and c(1) with true solution u(2) Infinity norm of the error at the grid points for various methods and numbers of interior grid points M M= 1st order finite difference 2nd order finite difference Linear finite elements Quadratic finite elements 9 8.9200e-02 8.9200e-02 8.6564e-02 8.6570e-02 99 9.5538e-02 9.5538e-02 9.5219e-02 9.5224e-02 999 9.6120e-02 9.6120e-02 9.6086e-02 9.6088e-02 PROBLEM 7 Using coefficient functions a(1) and c(1) with true solution u(3) ...
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