20060206 060825.000 TOMS352_PRB Test TOMS algorithm 352, which finds the characteristic values and associated solutions of Matthieu's differential equation. TEST01 Test BESSEL, which can compute J0 Bessel functions. X Exact Value Computed -5.0000 -0.17759677 -0.17759677 -4.0000 -0.39714981 -0.39714981 -3.0000 -0.26005195 -0.26005195 -2.0000 0.22389078 0.22389078 -1.0000 0.76519769 0.76519769 0.0000 1.0000000 1.0000000 1.0000 0.76519769 0.76519769 2.0000 0.22389078 0.22389078 3.0000 -0.26005195 -0.26005195 4.0000 -0.39714981 -0.39714981 5.0000 -0.17759677 -0.17759677 6.0000 0.15064526 0.15064526 7.0000 0.30007927 0.30007927 8.0000 0.17165081 0.17165081 9.0000 -0.90333611E-01 -0.90333611E-01 10.0000 -0.24593576 -0.24593576 11.0000 -0.17119030 -0.17119030 12.0000 0.47689311E-01 0.47689311E-01 13.0000 0.20692610 0.20692610 14.0000 0.17107348 0.17107348 15.0000 -0.14224473E-01 -0.14224473E-01 TEST02 Test BESSEL, which can compute J1 Bessel functions. X Exact Value Computed -5.0000 0.32757914 0.32757914 -4.0000 0.66043328E-01 0.66043328E-01 -3.0000 -0.33905896 -0.33905896 -2.0000 -0.57672481 -0.57672481 -1.0000 -0.44005059 -0.44005059 0.0000 0.0000000 0.0000000 1.0000 0.44005059 0.44005059 2.0000 0.57672481 0.57672481 3.0000 0.33905896 0.33905896 4.0000 -0.66043328E-01 -0.66043328E-01 5.0000 -0.32757914 -0.32757914 6.0000 -0.27668386 -0.27668386 7.0000 -0.46828235E-02 -0.46828235E-02 8.0000 0.23463635 0.23463635 9.0000 0.24531179 0.24531179 10.0000 0.43472746E-01 0.43472746E-01 11.0000 -0.17678530 -0.17678530 12.0000 -0.22344710 -0.22344710 13.0000 -0.70318052E-01 -0.70318052E-01 14.0000 0.13337515 0.13337515 15.0000 0.20510404 0.20510404 TEST03 Test BESSEL, which can compute Y0 Bessel functions. X Exact Value Computed 0.1000 -1.5342387 -1.5342387 1.0000 0.88256964E-01 0.88256964E-01 2.0000 0.51037567 0.51037567 3.0000 0.37685001 0.37685001 4.0000 -0.16940739E-01 -0.16940739E-01 5.0000 -0.30851763 -0.30851763 6.0000 -0.28819468 -0.28819468 7.0000 -0.25949744E-01 -0.25949744E-01 8.0000 0.22352149 0.22352149 9.0000 0.24993670 0.24993670 10.0000 0.55671167E-01 0.55671167E-01 11.0000 -0.16884732 -0.16884732 12.0000 -0.22523731 -0.22523731 13.0000 -0.78207865E-01 -0.78207865E-01 14.0000 0.12719257 0.12719257 15.0000 0.20546430 0.20546430 TEST04 Test BESSEL, which can compute Y1 Bessel functions. X Exact Value Computed 0.1000 -6.4589511 -6.4589511 1.0000 -0.78121282 -0.78121282 2.0000 -0.10703243 -0.10703243 3.0000 0.32467442 0.32467442 4.0000 0.39792571 0.39792571 5.0000 0.14786314 0.14786314 6.0000 -0.17501034 -0.17501034 7.0000 -0.30266724 -0.30266724 8.0000 -0.15806046 -0.15806046 9.0000 0.10431458 0.10431458 10.0000 0.24901542 0.24901542 11.0000 0.16370554 0.16370554 12.0000 -0.57099218E-01 -0.57099218E-01 13.0000 -0.21008141 -0.21008141 14.0000 -0.16664484 -0.16664484 15.0000 0.21073628E-01 0.21073628E-01 TEST05 Test MFCVAL, which can compute the eigenvalues and eigensolutions of Mathieu's differential equation. Here, we work with EVEN solutions. R Q Exact Value Computed 0 0 0.0000000 0.0000000 1 0 1.0000000 1.0000000 2 0 4.0000000 4.0000000 15 0 225.00000 225.00000 5 0 25.000000 25.000000 5 5 25.549972 25.549972 5 10 27.703769 27.703769 5 15 31.957821 31.957821 5 20 36.644990 36.644990 5 25 40.050191 40.050191 0 5 -5.8000460 -5.8000460 0 25 -40.256780 -40.256780 1 20 -14.491301 -14.491301 2 15 5.0779832 5.0779832 10 10 100.50677 100.50677 TEST06 Test MFCVAL, which can compute the eigenvalues and eigensolutions of Mathieu's differential equation. Here, we work with ODD solutions. R Q Exact Value Computed 1 0 1.0000000 1.0000000 1 25 -40.256779 -40.256779 2 0 4.0000000 4.0000000 2 5 2.0994604 2.0994604 2 10 -2.3821582 -2.3821582 2 15 -8.0993468 -8.0993468 2 20 -14.491063 -14.491063 2 25 -21.314861 -21.314861 5 15 27.967881 27.967881 10 0 100.00000 100.00000 10 10 100.50677 100.50677 15 0 225.00000 225.00000 15 20 225.89515 225.89515 TOMS352_PRB Normal end of execution. 20060206 060825.000