17 September 2021 9:31:12.720 AM FEM1D_PMETHOD FORTRAN90 version Solve the two-point boundary value problem - d/dX (P dU/dX) + Q U = F on the interval [-1,1], with U(-1) = U(1) = 0. The P method is used, which represents U as a weighted sum of orthogonal polynomials. Highest degree polynomial to use is 2 Number of points to be used for output = 0 Problem #2: U=cos(0.5*pi*x), P=1, Q=0, F=0.25*pi*pi*cos(0.5*pi*x) Basis function orthogonality test: i j b(i,j)/a(i) 0 0 1.00000 0 1 0.208167E-16 0 2 -0.832667E-16 1 0 0.346945E-16 1 1 1.00000 1 2 0.173472E-16 2 0 -0.303577E-15 2 1 0.379471E-16 2 2 1.00000 Representation of solution: Basis function coefficients: 0 0.954930 1 -0.125361E-17 2 -0.220787 X Approximate Solution -1.00000 0.00000 -0.800000 0.308802 -0.600000 0.588546 -0.400000 0.809559 -0.200000 0.950645 0.00000 0.999087 0.200000 0.950645 0.400000 0.809559 0.600000 0.588546 0.800000 0.308802 1.00000 0.00000 Comparison of computed and exact solutions: X U computed U exact Difference -1.0000 0.00000 0.612323E-16 0.612323E-16 -0.8000 0.308802 0.309017 0.214907E-03 -0.6000 0.588546 0.587785 -0.761186E-03 -0.4000 0.809559 0.809017 -0.542347E-03 -0.2000 0.950645 0.951057 0.411230E-03 0.0000 0.999087 1.00000 0.913031E-03 0.2000 0.950645 0.951057 0.411230E-03 0.4000 0.809559 0.809017 -0.542347E-03 0.6000 0.588546 0.587785 -0.761186E-03 0.8000 0.308802 0.309017 0.214907E-03 1.0000 0.00000 0.612323E-16 0.612323E-16 Big L2 error = 0.572595E-03 FEM1D_PMETHOD Normal end of execution. 17 September 2021 9:31:12.720 AM