03 March 2022 08:13:04 PM RKF45_TEST C version Test the RKF45 library. TEST01 Solve a scalar equation using R4_RKF: Y' = 0.25 * Y * ( 1 - Y / 20 ) FLAG T Y Y' Y_Exact Error 1 0.000000 1.000000 0.237500 1.000000 0.000000 2 4.000000 2.503204 0.547476 2.503220 -0.000016 2 8.000000 5.600052 1.008006 5.600091 -0.000040 2 12.000000 10.278066 1.249033 10.277734 0.000332 2 16.000000 14.836786 0.957569 14.836826 -0.000040 2 20.000000 17.730972 0.502901 17.730167 0.000805 TEST02 Solve a vector equation using R4_RKF: 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 0.000000 1.000000 0.000000 2 0.523599 0.866026 -0.500000 2 1.047198 0.500016 -0.866037 2 1.570796 0.000015 -1.000035 2 2.094395 -0.500007 -0.866082 2 2.617994 -0.866071 -0.500061 2 3.141593 -1.000087 -0.000037 2 3.665192 -0.866138 0.500013 2 4.188790 -0.500106 0.866104 2 4.712389 -0.000060 1.000138 2 5.235988 0.500020 0.866193 2 5.759587 0.866138 0.500151 2 6.283185 1.000190 0.000082 TEST03 Solve a scalar equation using R4_RKF: Y' = 0.25 * Y * ( 1 - Y / 20 ) This routine uses the SINGLE STEP mode. FLAG T Y Y' Y_Exact Error -1 0.000000 1.000000 0.237500 1.000000 0.000000 -2 0.310960 1.076490 0.254637 1.076490 0.000000 -2 1.865759 1.548298 0.357109 1.548300 -0.000002 2 4.000000 2.503204 0.547476 2.503220 -0.000016 -2 6.000000 3.817148 0.772154 3.817178 -0.000030 2 8.000000 5.600052 1.008006 5.600091 -0.000040 2 12.000000 10.278066 1.249033 10.277734 0.000332 2 16.000000 14.836786 0.957569 14.836826 -0.000040 2 20.000000 17.730972 0.502901 17.730167 0.000805 TEST04 Solve a scalar equation using R8_RKF: Y' = 0.25 * Y * ( 1 - Y / 20 ) FLAG T Y Y' Y_Exact Error 1 0.000000 1.000000 0.237500 1.000000 0.000000 2 4.000000 2.503220 0.547479 2.503220 0.000000 2 8.000000 5.600091 1.008010 5.600091 -0.000000 2 12.000000 10.277734 1.249036 10.277734 -0.000000 2 16.000000 14.836827 0.957564 14.836826 0.000000 2 20.000000 17.730166 0.503057 17.730167 -0.000001 TEST05 Solve a vector equation using R8_RKF: Y'(1) = Y(2) Y'(2) = -Y(1) FLAG T Y(1) Y(2) 1 0.000000 1.000000 0.000000 2 0.523599 0.866025 -0.500000 2 1.047198 0.500000 -0.866025 2 1.570796 0.000000 -1.000000 2 2.094395 -0.500000 -0.866025 2 2.617994 -0.866025 -0.500000 2 3.141593 -1.000000 -0.000000 2 3.665191 -0.866025 0.500000 2 4.188790 -0.500000 0.866025 2 4.712389 -0.000000 1.000000 2 5.235988 0.500000 0.866025 2 5.759587 0.866025 0.500000 2 6.283185 1.000000 0.000000 TEST06 Solve a scalar equation using R8_RKF: Y' = 0.25 * Y * ( 1 - Y / 20 ) This routine uses the SINGLE STEP mode. FLAG T Y Y' Y_Exact Error -1 0.000000 1.000000 0.237500 1.000000 0.000000 -2 0.041660 1.009941 0.239735 1.009941 -0.000000 -2 0.249959 1.061062 0.251192 1.061062 0.000000 -2 0.713324 1.183667 0.278403 1.183667 0.000000 -2 1.180501 1.320626 0.308356 1.320626 0.000000 -2 1.647719 1.472207 0.340959 1.472207 0.000000 -2 2.115781 1.639976 0.376375 1.639976 -0.000000 -2 2.585631 1.825723 0.414765 1.825723 0.000000 -2 3.058299 2.031467 0.456281 2.031466 0.000000 -2 3.529150 2.256606 0.500498 2.256606 -0.000000 2 4.000000 2.503220 0.547479 2.503220 0.000000 -2 4.488220 2.782961 0.598929 2.782961 -0.000000 -2 4.984780 3.093895 0.653821 3.093895 0.000000 -2 5.491613 3.439951 0.712072 3.439951 0.000000 -2 6.011100 3.825756 0.773484 3.825756 0.000000 -2 6.546184 4.256793 0.837695 4.256793 0.000000 -2 7.100597 4.739668 0.904111 4.739668 -0.000000 -2 7.550299 5.158183 0.956960 5.158183 -0.000000 2 8.000000 5.600091 1.008010 5.600091 -0.000000 -2 8.636956 6.264005 1.075529 6.264004 0.000000 -2 9.315213 7.015494 1.138659 7.015494 -0.000000 -2 10.064284 7.890322 1.194366 7.890323 -0.000000 -2 10.932839 8.947763 1.236160 8.947763 -0.000000 2 12.000000 10.277734 1.249036 10.277734 -0.000000 -2 13.064868 11.595150 1.218194 11.595150 -0.000000 -2 14.062311 12.780518 1.153359 12.780519 -0.000000 -2 15.031156 13.856458 1.064097 13.856458 0.000000 -2 15.851518 14.693374 0.974653 14.693374 0.000001 2 16.000000 14.836827 0.957564 14.836826 0.000000 -2 16.742410 15.515329 0.869764 15.515328 0.000001 -2 17.488264 16.130626 0.780193 16.130627 -0.000001 -2 18.199253 16.655363 0.696327 16.655363 0.000000 -2 18.888597 17.108278 0.618405 17.108278 -0.000001 -2 19.444298 17.435256 0.558962 17.435255 0.000001 2 20.000000 17.730166 0.503057 17.730167 -0.000001 RKF45_TEST Normal end of execution. 03 March 2022 08:13:04 PM