5 April 2011 9:31:56.135 AM RKF45_PRB FORTRAN77 version Test the RKF45 library. TEST01 Solve a scalar equation using RKF_S: Y' = 0.25 * Y * ( 1 - Y / 20 ) FLAG T Y Y_Exact Error 1 0.00000 1.00000 1.00000 0.00000 2 4.00000 2.50320 2.50322 -0.162125E-04 2 8.00000 5.60005 5.60009 -0.395775E-04 2 12.0000 10.2781 10.2777 0.331879E-03 2 16.0000 14.8368 14.8368 -0.400543E-04 2 20.0000 17.7310 17.7302 0.806808E-03 TEST02 Solve a vector equation using RKF_S: Y'(1) = Y(2) Y'(2) = -Y(1) This system is equivalent to the following second order system: Z" = - Z. FLAG T Y(1) Y(2) 1 0.00000 1.00000 0.00000 2 0.523599 0.866026 -0.500000 2 1.04720 0.500016 -0.866037 2 1.57080 0.151396E-04 -1.00004 2 2.09440 -0.500007 -0.866082 2 2.61799 -0.866071 -0.500061 2 3.14159 -1.00009 -0.374317E-04 2 3.66519 -0.866138 0.500013 2 4.18879 -0.500106 0.866104 2 4.71239 -0.599027E-04 1.00014 2 5.23599 0.500020 0.866193 2 5.75959 0.866138 0.500151 2 6.28319 1.00019 0.820756E-04 TEST03 Solve a scalar equation using RKF_S: Y' = 0.25 * Y * ( 1 - Y / 20 ) Use the special SINGLE_STEP mode which returns after every step. FLAG T Y Y_Exact Error -1 0.00000 1.00000 1.00000 0.00000 -2 0.310960 1.07649 1.07649 0.00000 -2 1.86576 1.54830 1.54830 -0.202656E-05 2 4.00000 2.50320 2.50322 -0.162125E-04 -2 6.00000 3.81715 3.81718 -0.293255E-04 2 8.00000 5.60005 5.60009 -0.395775E-04 2 12.0000 10.2781 10.2777 0.331879E-03 2 16.0000 14.8368 14.8368 -0.400543E-04 2 20.0000 17.7310 17.7302 0.806808E-03 TEST04 Solve a scalar equation using RKF_D: Y' = 0.25 * Y * ( 1 - Y / 20 ) FLAG T Y Y_Exact Error 1 0.00000 1.00000 1.00000 0.00000 2 4.00000 2.50322 2.50322 -0.197948E-07 2 8.00000 5.60009 5.60009 -0.533362E-07 2 12.0000 10.2777 10.2777 -0.136559E-07 2 16.0000 14.8368 14.8368 -0.129675E-06 2 20.0000 17.7302 17.7302 -0.148695E-07 TEST05 Solve a vector equation using RKF_D: Y'(1) = Y(2) Y'(2) = -Y(1) FLAG T Y(1) Y(2) 1 0.00000 1.00000 0.00000 2 0.523599 0.866025 -0.500000 2 1.04720 0.500000 -0.866025 2 1.57080 0.282746E-08 -1.00000 2 2.09440 -0.500000 -0.866025 2 2.61799 -0.866025 -0.500000 2 3.14159 -1.00000 -0.566233E-08 2 3.66519 -0.866025 0.500000 2 4.18879 -0.500000 0.866025 2 4.71239 -0.849719E-08 1.00000 2 5.23599 0.500000 0.866025 2 5.75959 0.866025 0.500000 2 6.28319 1.00000 0.113321E-07 TEST06 Solve a scalar equation using RKF_D: Y' = 0.25 * Y * ( 1 - Y / 20 ) Use the special SINGLE_STEP mode which returns after every step. FLAG T Y Y_Exact Error -1 0.00000 1.00000 1.00000 0.00000 -2 0.416598E-01 1.00994 1.00994 -0.888178E-15 -2 0.249959 1.06106 1.06106 -0.121079E-10 -2 0.713324 1.18367 1.18367 -0.149659E-08 -2 1.18050 1.32063 1.32063 -0.329375E-08 -2 1.64772 1.47221 1.47221 -0.534727E-08 -2 2.11578 1.63998 1.63998 -0.768026E-08 -2 2.58563 1.82572 1.82572 -0.103172E-07 -2 3.05830 2.03147 2.03147 -0.132813E-07 -2 3.52915 2.25661 2.25661 -0.164369E-07 2 4.00000 2.50322 2.50322 -0.197948E-07 -2 4.48822 2.78296 2.78296 -0.237885E-07 -2 4.98478 3.09390 3.09390 -0.281367E-07 -2 5.49161 3.43995 3.43995 -0.328021E-07 -2 6.01110 3.82576 3.82576 -0.377093E-07 -2 6.54618 4.25679 4.25679 -0.427215E-07 -2 7.10060 4.73967 4.73967 -0.476053E-07 -2 7.55030 5.15818 5.15818 -0.506073E-07 2 8.00000 5.60009 5.60009 -0.533362E-07 -2 8.63696 6.26400 6.26400 -0.554371E-07 -2 9.31521 7.01549 7.01549 -0.545314E-07 -2 10.0643 7.89032 7.89032 -0.480742E-07 -2 10.9328 8.94776 8.94776 -0.312272E-07 2 12.0000 10.2777 10.2777 -0.136559E-07 -2 13.0649 11.5951 11.5951 -0.579265E-07 -2 14.0623 12.7805 12.7805 -0.109661E-06 -2 15.0312 13.8565 13.8565 -0.140558E-06 -2 15.8515 14.6934 14.6934 -0.131989E-06 2 16.0000 14.8368 14.8368 -0.129675E-06 -2 16.7424 15.5153 15.5153 -0.110159E-06 -2 17.4883 16.1306 16.1306 -0.825894E-07 -2 18.1993 16.6554 16.6554 -0.560094E-07 -2 18.8886 17.1083 17.1083 -0.315194E-07 -2 19.4443 17.4353 17.4353 -0.230014E-07 2 20.0000 17.7302 17.7302 -0.148695E-07 RKF45_PRB Normal end of execution. 5 April 2011 9:31:56.137 AM