17 September 2021 9:31:09.908 AM FD1D_BVP_TEST FORTRAN90 version Test the FD1D_BVP library. FD1D_BVP_TEST01 A1(X) = 1.0 A1'(X) = 0.0 C1(X) = 0.0 F1(X) = X * ( X + 3 ) * exp ( X ) U1(X) = X * ( 1 - X ) * exp ( X ) Number of nodes = 21 X1 = 0.00000 X2 = 1.00000 I X U Uexact Error 1 0.0000 0.0000 0.0000 0.00000 2 0.0500 0.0499 0.0499 0.798361E-04 3 0.1000 0.0993 0.0995 0.155098E-03 4 0.1500 0.1479 0.1481 0.225345E-03 5 0.2000 0.1951 0.1954 0.290100E-03 6 0.2500 0.2404 0.2408 0.348849E-03 7 0.3000 0.2831 0.2835 0.401035E-03 8 0.3500 0.3224 0.3228 0.446054E-03 9 0.4000 0.3576 0.3580 0.483258E-03 10 0.4500 0.3876 0.3882 0.511944E-03 11 0.5000 0.4116 0.4122 0.531355E-03 12 0.5500 0.4284 0.4290 0.540674E-03 13 0.6000 0.4368 0.4373 0.539021E-03 14 0.6500 0.4353 0.4358 0.525445E-03 15 0.7000 0.4224 0.4229 0.498924E-03 16 0.7500 0.3965 0.3969 0.458356E-03 17 0.8000 0.3557 0.3561 0.402556E-03 18 0.8500 0.2980 0.2983 0.330247E-03 19 0.9000 0.2211 0.2214 0.240054E-03 20 0.9500 0.1227 0.1228 0.130502E-03 21 1.0000 0.0000 0.0000 0.00000 Repeat, using a nonuniform mesh. I X U Uexact Error 1 0.0000 0.0000 0.0000 0.00000 2 0.2236 0.2234 0.2171 0.628899E-02 3 0.3162 0.3027 0.2967 0.607910E-02 4 0.3873 0.3552 0.3495 0.569736E-02 5 0.4472 0.3919 0.3866 0.528898E-02 6 0.5000 0.4171 0.4122 0.488315E-02 7 0.5477 0.4329 0.4284 0.448769E-02 8 0.5916 0.4407 0.4366 0.410458E-02 9 0.6325 0.4413 0.4375 0.373387E-02 10 0.6708 0.4353 0.4319 0.337496E-02 11 0.7071 0.4231 0.4200 0.302705E-02 12 0.7416 0.4050 0.4023 0.268933E-02 13 0.7746 0.3812 0.3788 0.236100E-02 14 0.8062 0.3519 0.3499 0.204135E-02 15 0.8367 0.3172 0.3155 0.172974E-02 16 0.8660 0.2773 0.2758 0.142557E-02 17 0.8944 0.2321 0.2310 0.112834E-02 18 0.9220 0.1817 0.1809 0.837561E-03 19 0.9487 0.1263 0.1257 0.552825E-03 20 0.9747 0.0657 0.0654 0.273752E-03 21 1.0000 0.0000 0.0000 0.00000 FD1D_BVP_TEST02 A1(X) = 1.0 A1'(X) = 0.0 C2(X) = 2.0 F2(X) = X * ( 5 - X ) * exp ( X ) U1(X) = X * ( 1 - X ) * exp ( X ) Number of nodes = 11 X1 = 0.00000 X2 = 1.00000 I X U Uexact Error 1 0.0000 0.0000 0.0000 0.00000 2 0.1000 0.0990 0.0995 0.509024E-03 3 0.2000 0.1945 0.1954 0.947935E-03 4 0.3000 0.2822 0.2835 0.130963E-02 5 0.4000 0.3565 0.3580 0.158279E-02 6 0.5000 0.4104 0.4122 0.175124E-02 7 0.6000 0.4355 0.4373 0.179313E-02 8 0.7000 0.4212 0.4229 0.168002E-02 9 0.8000 0.3547 0.3561 0.137563E-02 10 0.9000 0.2205 0.2214 0.834439E-03 11 1.0000 0.0000 0.0000 0.00000 FD1D_BVP_TEST03 A1(X) = 1.0 A1'(X) = 0.0 C3(X) = 2.0 * X F3(X) = - X * ( 2 * X * X - 3 * X - 3 ) * exp ( X ) U1(X) = X * ( 1 - X ) * exp ( X ) Number of nodes = 11 X1 = 0.00000 X2 = 1.00000 I X U Uexact Error 1 0.0000 0.0000 0.0000 0.00000 2 0.1000 0.0989 0.0995 0.568213E-03 3 0.2000 0.1944 0.1954 0.105727E-02 4 0.3000 0.2820 0.2835 0.145438E-02 5 0.4000 0.3563 0.3580 0.174549E-02 6 0.5000 0.4103 0.4122 0.191419E-02 7 0.6000 0.4354 0.4373 0.194046E-02 8 0.7000 0.4211 0.4229 0.179915E-02 9 0.8000 0.3546 0.3561 0.145814E-02 10 0.9000 0.2205 0.2214 0.876155E-03 11 1.0000 0.0000 0.0000 0.00000 FD1D_BVP_TEST04 A2(X) = 1.0 + X * X A2'(X) = 2.0 * X C1(X) = 0.0 F4(X) = ( X + 3 X^2 + 5 X^3 + X^4 ) * exp ( X ) U1(X) = X * ( 1 - X ) * exp ( X ) Number of nodes = 11 X1 = 0.00000 X2 = 1.00000 I X U Uexact Error 1 0.0000 0.0000 0.0000 0.00000 2 0.1000 0.0984 0.0995 0.108537E-02 3 0.2000 0.1934 0.1954 0.205725E-02 4 0.3000 0.2806 0.2835 0.286700E-02 5 0.4000 0.3546 0.3580 0.346628E-02 6 0.5000 0.4084 0.4122 0.380810E-02 7 0.6000 0.4335 0.4373 0.384652E-02 8 0.7000 0.4194 0.4229 0.353540E-02 9 0.8000 0.3533 0.3561 0.282654E-02 10 0.9000 0.2197 0.2214 0.166760E-02 11 1.0000 0.0000 0.0000 0.00000 FD1D_BVP_TEST05 A3(X) = 1.0 + X * X for X <= 1/3 = 7/9 + X for 1/3 < X A3'(X) = 2.0 * X for X <= 1/3 1 for 1/3 < X C1(X) = 0.0 F5(X) = ( X + 3 X^2 + 5 X^3 + X^4 ) * exp ( X ) for X <= 1/3 = ( - 1 + 10/3 X + 43/9 X^2 + X^3 ) * exp ( X ) for 1/3 <= X U1(X) = X * ( 1 - X ) * exp ( X ) Number of nodes = 11 X1 = 0.00000 X2 = 1.00000 I X U Uexact Error 1 0.0000 0.0000 0.0000 0.00000 2 0.1000 0.0984 0.0995 0.104668E-02 3 0.2000 0.1934 0.1954 0.198062E-02 4 0.3000 0.2807 0.2835 0.275386E-02 5 0.4000 0.3547 0.3580 0.331859E-02 6 0.5000 0.4086 0.4122 0.360183E-02 7 0.6000 0.4337 0.4373 0.358904E-02 8 0.7000 0.4196 0.4229 0.325746E-02 9 0.8000 0.3535 0.3561 0.257627E-02 10 0.9000 0.2199 0.2214 0.150638E-02 11 1.0000 0.0000 0.0000 0.00000 FD1D_BVP_TEST Normal end of execution. 17 September 2021 9:31:09.909 AM