24 February 2023 6:43:21.474 PM FILON_TEST FORTRAN90 version Test FILON. TEST01 FILON_TAB_COS estimates the integral of. F(X) * COS ( T * X ) Use integrands F(X)=1, X, X^2. A = 0.000000000000000 B = 6.283185307179586 N = 11 T Approximate Exact 1.000000000000000 -0.1905476522093207E-15 -0.2449293598294706E-15 1.000000000000000 -0.1322518650155724E-14 -0.1554312234475219E-14 1.000000000000000 12.56637061435916 12.56637061435916 2.000000000000000 -0.2590075573475023E-15 -0.2449293598294706E-15 2.000000000000000 -0.1465504961912174E-14 -0.1526556658859590E-14 2.000000000000000 3.141592653589786 3.141592653589784 10.00000000000000 -0.2790294798406905E-15 -0.2449293598294706E-15 10.00000000000000 -0.1534662139123798E-14 -0.1538769112130467E-14 10.00000000000000 0.1256637061435835 0.1256637061435820 TEST02 Integrate F(X) = log(1+X)*cos(T*X): Supply integrand as a table. T = 10, and N increases N Approximate Exact Error 21 -0.8478417820979797E-02 -0.8446594405000001E-02 -0.31823416E-04 41 -0.8478417820986149E-02 -0.8446594405000001E-02 -0.31823416E-04 81 -0.8448264693952125E-02 -0.8446594405000001E-02 -0.16702890E-05 161 -0.8446693873063937E-02 -0.8446594405000001E-02 -0.99468064E-07 321 -0.8446600545717286E-02 -0.8446594405000001E-02 -0.61407173E-08 641 -0.8446594787479611E-02 -0.8446594405000001E-02 -0.38247961E-09 TEST03 Integrate F(X)=log(1+X)*cos(T*X): Supply integrand as a function. T = 10, and N increases N Approximate Exact Error 21 -0.8478417820979797E-02 -0.8446594405000001E-02 -0.31823416E-04 41 -0.8478417820986149E-02 -0.8446594405000001E-02 -0.31823416E-04 81 -0.8448264693952125E-02 -0.8446594405000001E-02 -0.16702890E-05 161 -0.8446693873063937E-02 -0.8446594405000001E-02 -0.99468064E-07 321 -0.8446600545717286E-02 -0.8446594405000001E-02 -0.61407173E-08 641 -0.8446594787479611E-02 -0.8446594405000001E-02 -0.38247961E-09 TEST04 FILON_TAB_SIN estimates the integral of. F(X) * SIN ( T * X ) Use integrands 1, X, X^2. A = 0.000000000000000 B = 6.283185307179586 N = 11 T Approximate Exact 1.000000000000000 0.8425908742155465E-16 0.000000000000000 1.000000000000000 -6.283185307179585 -6.283185307179586 1.000000000000000 -39.47841760435743 -39.47841760435743 2.000000000000000 -0.3509817438266788E-16 0.000000000000000 2.000000000000000 -3.141592653589794 -3.141592653589793 2.000000000000000 -19.73920880217872 -19.73920880217872 10.00000000000000 0.6195699061366312E-31 0.000000000000000 10.00000000000000 -0.6283185307179586 -0.6283185307179586 10.00000000000000 -3.947841760435743 -3.947841760435744 TEST05 Integrate F(X)=log(1+X)*sin(T*X): Supply integrand as a table. T = 10, and N increases N Approximate Exact Error 21 -0.1985568308709911 -0.1976268077187200 -0.93002315E-03 41 -0.1976282136646625 -0.1976268077187200 -0.14059459E-05 81 -0.1976265585745937 -0.1976268077187200 0.24914413E-06 161 -0.1976267885345487 -0.1976268077187200 0.19184171E-07 321 -0.1976268064687506 -0.1976268077187200 0.12499694E-08 641 -0.1976268076398181 -0.1976268077187200 0.78901857E-10 TEST06 Integrate F(X)=log(1+X)*sin(T*X): Supply integrand as a function. T = 10, and N increases N Approximate Exact Error 21 -0.1985568308709911 -0.1976268077187200 -0.93002315E-03 41 -0.1976282136646625 -0.1976268077187200 -0.14059459E-05 81 -0.1976265585745937 -0.1976268077187200 0.24914413E-06 161 -0.1976267885345487 -0.1976268077187200 0.19184171E-07 321 -0.1976268064687506 -0.1976268077187200 0.12499694E-08 641 -0.1976268076398181 -0.1976268077187200 0.78901857E-10 FILON_TEST Normal end of execution. 24 February 2023 6:43:21.474 PM