19 January 2020 09:15:21 AM DIFFER_TEST: C version Test the DIFFER library. TEST01 Demonstrate that the DIFFER matrix is 'really' a Vandermonde matrix. Stencil matrix: Col: 0 1 2 3 Row 0: 2.5 3.3 -1.3 0.5 1: 6.25 10.89 1.69 0.25 2: 15.625 35.937 -2.197 0.125 3: 39.0625 118.592 2.8561 0.0625 Solution of DIFFER system: 0: 1 1: 2 2: 3 3: 4 Solution of VANDERMONDE system: 0: 2.5 1: 6.6 2: -3.9 3: 2 Transformed solution of VANDERMONDE system: 0: 1 1: 2 2: 3 3: 4 TEST02 DIFFER_INVERSE returns the inverse of a DIFFER matrix; N Inverse error 2 0 2 4.44089e-16 2 8.88185e-16 2 4.44089e-16 2 0 3 1.17776e-14 3 1.65635e-13 3 2.87917e-15 3 5.12266e-14 3 1.8897e-14 4 3.14213e-14 4 8.5015e-14 4 5.71398e-14 4 4.28707e-14 4 2.80585e-12 5 1.43579e-10 5 1.45624e-12 5 1.81003e-11 5 2.30649e-12 5 1.19425e-11 6 8.31044e-10 6 8.46168e-11 6 7.55719e-12 6 7.24273e-12 6 1.81026e-11 7 4.73678e-10 7 5.59992e-11 7 5.32315e-10 7 2.01382e-11 7 3.07994e-11 8 5.89396e-10 8 5.9282e-10 8 9.3962e-09 8 1.04455e-09 8 1.7787e-09 TEST03 Reproduce a specific example. Solution of DIFFER system: 0: -0.0833333 1: 0.5 2: -1.5 3: 0.25 DFDX = 3.66931 d exp(x) /dx = 3.6693 TEST04 DIFFER_FORWARD, DIFFER_BACKWARD, and DIFFER_CENTRAL produce coefficients for difference approximations of the O-th derivative, with error of order H^P, for a uniform spacing of H. Use a spacing of H = 1 for all examples. Forward difference coefficients, O = 3 P = 1 0: 0 -1 1: 1 3 2: 2 -3 3: 3 1 Backward difference coefficients, O = 3 P = 1 0: -3 -1 1: -2 3 2: -1 -3 3: 0 1 Central difference coefficients, O = 3 P = 2 0: -2 -0.5 1: -1 1 2: 0 0 3: 1 -1 4: 2 0.5 Central difference coefficients, O = 3 P = 4 0: -3 0.125 1: -2 -1 2: -1 1.625 3: 0 0 4: 1 -1.625 5: 2 1 6: 3 -0.125 Forward difference coefficients, O = 4 P = 1 0: 0 1 1: 1 -4 2: 2 6 3: 3 -4 4: 4 1 Backward difference coefficients, O = 4 P = 1 0: -4 1 1: -3 -4 2: -2 6 3: -1 -4 4: 0 1 Central difference coefficients, O = 4 P = 3 0: -3 -0.166667 1: -2 2 2: -1 -6.5 3: 0 9.33333 4: 1 -6.5 5: 2 2 6: 3 -0.166667 TEST05 DIFFER_STENCIL produces coefficients for difference approximations of the O-th derivative, using arbitrarily spaced data, with maximum spacing H with error of order H^P. Use a spacing of H = 1 for all examples. Forward difference coefficients, O = 3 P = 1 0: 0 -1 1: 1 3 2: 2 -3 3: 3 1 Backward difference coefficients, O = 3 P = 1 0: -3 -1 1: -2 3 2: -1 -3 3: 0 1 Central difference coefficients, O = 3 P = 2 0: -2 -0.5 1: -1 1 2: 0 0 3: 1 -1 4: 2 0.5 Central difference coefficients, O = 3 P = 4 0: -3 0.125 1: -2 -1 2: -1 1.625 3: 0 0 4: 1 -1.625 5: 2 1 6: 3 -0.125 Forward difference coefficients, O = 4 P = 1 0: 0 1 1: 1 -4 2: 2 6 3: 3 -4 4: 4 1 Backward difference coefficients, O = 4 P = 1 0: -4 1 1: -3 -4 2: -2 6 3: -1 -4 4: 0 1 Central difference coefficients, O = 4 P = 3 0: -3 -0.166667 1: -2 2 2: -1 -6.5 3: 0 9.33333 4: 1 -6.5 5: 2 2 6: 3 -0.166667 DIFFER_TEST: Normal end of execution. 19 January 2020 09:15:21 AM