>> quadrature_test_2d ( 'gl_d2_1x1' ) 29-Jan-2009 09:35:09 QUADRATURE_TEST_2D MATLAB version Investigate the accuracy of a 2D quadrature rule by integrating test functions. QUADRATURE_TEST_2D: User input: Quadrature rule X file = "gl_d2_1x1_x.txt". Quadrature rule W file = "gl_d2_1x1_w.txt". Quadrature rule R file = "gl_d2_1x1_r.txt". Spatial dimension = 2 Number of points = 1 Prob Dim Points Approx Exact Error 1 2 1 1.333333 1.644934 0.311601 2 2 1 4.000000 4.355172 0.355172 3 2 1 2.828427 3.124194 0.295767 4 2 1 2.309401 2.579008 0.269606 5 2 1 0.500000 0.444444 0.055556 6 2 1 1.000000 1.863016 0.863016 7 2 1 0.000000 0.533333 0.533333 QUADRATURE_TEST_2D: Normal end of execution. 29-Jan-2009 09:35:09 >> >> quadrature_test_2d ( 'gl_d2_2x2' ) 29-Jan-2009 09:36:05 QUADRATURE_TEST_2D MATLAB version Investigate the accuracy of a 2D quadrature rule by integrating test functions. QUADRATURE_TEST_2D: User input: Quadrature rule X file = "gl_d2_2x2_x.txt". Quadrature rule W file = "gl_d2_2x2_w.txt". Quadrature rule R file = "gl_d2_2x2_r.txt". Spatial dimension = 2 Number of points = 4 Prob Dim Points Approx Exact Error 1 2 4 1.523077 1.644934 0.121857 2 2 4 4.242641 4.355172 0.112531 3 2 4 3.064894 3.124194 0.059301 4 2 4 2.518960 2.579008 0.060048 5 2 4 0.454124 0.444444 0.009680 6 2 4 1.666667 1.863016 0.196350 7 2 4 0.379918 0.533333 0.153415 QUADRATURE_TEST_2D: Normal end of execution. 29-Jan-2009 09:36:05 >> >> quadrature_test_2d ( 'gl_d2_4x4' ) 29-Jan-2009 09:36:22 QUADRATURE_TEST_2D MATLAB version Investigate the accuracy of a 2D quadrature rule by integrating test functions. QUADRATURE_TEST_2D: User input: Quadrature rule X file = "gl_d2_4x4_x.txt". Quadrature rule W file = "gl_d2_4x4_w.txt". Quadrature rule R file = "gl_d2_4x4_r.txt". Spatial dimension = 2 Number of points = 16 Prob Dim Points Approx Exact Error 1 2 16 1.605994 1.644934 0.038940 2 2 16 4.332078 4.355172 0.023095 3 2 16 3.114885 3.124194 0.009309 4 2 16 2.569215 2.579008 0.009792 5 2 16 0.445994 0.444444 0.001549 6 2 16 1.730718 1.863016 0.132298 7 2 16 0.471735 0.533333 0.061599 QUADRATURE_TEST_2D: Normal end of execution. 29-Jan-2009 09:36:22 >> >> quadrature_test_2d ( 'gl_d2_8x8' ) 29-Jan-2009 09:36:38 QUADRATURE_TEST_2D MATLAB version Investigate the accuracy of a 2D quadrature rule by integrating test functions. QUADRATURE_TEST_2D: User input: Quadrature rule X file = "gl_d2_8x8_x.txt". Quadrature rule W file = "gl_d2_8x8_w.txt". Quadrature rule R file = "gl_d2_8x8_r.txt". Spatial dimension = 2 Number of points = 64 Prob Dim Points Approx Exact Error 1 2 64 1.633892 1.644934 0.011042 2 2 64 4.351528 4.355172 0.003644 3 2 64 3.122856 3.124194 0.001338 4 2 64 2.577591 2.579008 0.001416 5 2 64 0.444670 0.444444 0.000225 6 2 64 1.858928 1.863016 0.004088 7 2 64 0.509617 0.533333 0.023716 QUADRATURE_TEST_2D: Normal end of execution. 29-Jan-2009 09:36:38 >> >> quadrature_test_2d ( 'gl_d2_16x16' ) 29-Jan-2009 09:36:53 QUADRATURE_TEST_2D MATLAB version Investigate the accuracy of a 2D quadrature rule by integrating test functions. QUADRATURE_TEST_2D: User input: Quadrature rule X file = "gl_d2_16x16_x.txt". Quadrature rule W file = "gl_d2_16x16_w.txt". Quadrature rule R file = "gl_d2_16x16_r.txt". Spatial dimension = 2 Number of points = 256 Prob Dim Points Approx Exact Error 1 2 256 1.641994 1.644934 0.002940 2 2 256 4.354665 4.355172 0.000508 3 2 256 3.124013 3.124194 0.000181 4 2 256 2.578815 2.579008 0.000192 5 2 256 0.444475 0.444444 0.000031 6 2 256 1.863128 1.863016 0.000112 7 2 256 0.524558 0.533333 0.008776 QUADRATURE_TEST_2D: Normal end of execution. 29-Jan-2009 09:36:53 >> >> quadrature_test_2d ( 'gl_d2_32x32' ) 29-Jan-2009 09:37:09 QUADRATURE_TEST_2D MATLAB version Investigate the accuracy of a 2D quadrature rule by integrating test functions. QUADRATURE_TEST_2D: User input: Quadrature rule X file = "gl_d2_32x32_x.txt". Quadrature rule W file = "gl_d2_32x32_w.txt". Quadrature rule R file = "gl_d2_32x32_r.txt". Spatial dimension = 2 Number of points = 1024 Prob Dim Points Approx Exact Error 1 2 1024 1.644175 1.644934 0.000759 2 2 1024 4.355105 4.355172 0.000067 3 2 1024 3.124171 3.124194 0.000024 4 2 1024 2.578982 2.579008 0.000025 5 2 1024 0.444448 0.444444 0.000004 6 2 1024 1.863199 1.863016 0.000183 7 2 1024 0.530158 0.533333 0.003176 QUADRATURE_TEST_2D: Normal end of execution. 29-Jan-2009 09:37:09 >>