
====================================================================================

               >>>   Example 1a - Talbot Suite DE   <<<

         Application of Talbot's method to solve the PDE equation

			u_t (x,t) = u_x (x,t),         x > X0,  t>0

	with conditions:
			u(x,0+) = x
			u(X0,t) = X0 + t


	The analytical solution is

		u(x,t) = x + t

	and its Laplace Transform is

		          1     x
		U(x,s) = --- + ---
		         s^2    s

	with a double pole at 0

	     and abscissa of convergence: sigma0 = 0

====================================================================================

	   Ex. 1a: output from ./2PAR/LTS2_ode/OMP_main_ACCURACY.c

	LT samples by solving ODE problems by means of ode.c

	      5 t in [100, 500],    9 x in [10, 20],    tol=1.000000e-012
====================================================================================


CHECK: NESTED PARALLELISM is not supported
                          Now it is supported

RELERR1 = [ % COARSE-GRAIN OMP PARALLELISM with 3 threads for modified Talbot's method
            8.425616e-012  8.255830e-015  7.334635e-016  2.356922e-015  6.687461e-016
            7.931254e-012  8.072438e-015  3.652589e-016  9.675476e-016  2.112518e-015
            7.447246e-012  9.496195e-015  1.273293e-015  2.893847e-015  4.214732e-015
            6.975375e-012  1.037143e-014  3.623485e-016  2.747718e-015  3.098035e-015
            6.512155e-012  1.004674e-014  9.022765e-016  1.369721e-015  5.960281e-015
            6.059508e-012  1.025153e-014  7.189681e-016  1.775290e-015  4.404333e-016
            5.616614e-012  1.149936e-014  8.951720e-016  2.314582e-015  6.590541e-016
            5.182325e-012  1.208329e-014  1.248326e-015  2.850655e-015  4.383107e-016
            4.757794e-012  1.201463e-014  1.065814e-015  1.894781e-015  8.745141e-016
          ];

RELERR2 = [ % FINE-GRAIN OMP PARALLELISM with 3 threads for modified Talbot's method
            8.425616e-012  8.255830e-015  7.334635e-016  1.386425e-015  5.015596e-015
            7.931254e-012  8.879682e-015  3.652589e-016  1.796874e-015  4.780962e-015
            7.447246e-012  9.496195e-015  5.456968e-016  3.858462e-015  2.218280e-016
            6.975375e-012  1.023846e-014  3.623485e-016  1.786017e-015  1.327729e-015
            6.512279e-012  1.017894e-014  0.000000e+000  2.191553e-015  5.077276e-015
            6.059386e-012  1.038296e-014  8.987102e-016  8.193646e-016  4.404333e-016
            5.616735e-012  1.149936e-014  8.951720e-016  3.131494e-015  6.590541e-016
            5.182444e-012  1.208329e-014  1.248326e-015  2.036182e-015  3.068175e-015
            4.757794e-012  1.291896e-014  1.065814e-015  1.894781e-015  4.372571e-015
          ];

RELERR3 = [ % NESTED COARSE/FINE-GRAIN OMP PARALLELISM with 3 (outer), 2 (inner) threads for modified Talbot's method
            8.426520e-012  8.255830e-015  7.334635e-016  1.386425e-015  9.473903e-015
            7.931254e-012  8.879682e-015  3.652589e-016  1.796874e-015  4.780962e-015
            7.447246e-012  9.496195e-015  5.456968e-016  2.067033e-015  1.996452e-015
            6.974500e-012  9.440661e-015  3.623485e-016  9.617013e-016  3.983188e-015
            6.512155e-012  1.004674e-014  9.022765e-016  3.150358e-015  6.622534e-016
            6.059508e-012  1.025153e-014  7.189681e-016  8.193646e-016  2.202166e-015
            5.616614e-012  1.149936e-014  8.951720e-016  2.314582e-015  1.098424e-015
            5.182325e-012  1.208329e-014  1.248326e-015  2.850655e-015  3.068175e-015
            4.757794e-012  1.291896e-014  1.065814e-015  1.894781e-015  3.498057e-015
          ];

ABSERR1 = [ % COARSE-GRAIN OMP PARALLELISM with 3 threads for modified Talbot's method
            9.268177e-010  1.733724e-012  2.273737e-013  9.663381e-013  3.410605e-013
            8.823520e-010  1.705303e-012  1.136868e-013  3.979039e-013  1.080025e-012
            8.378152e-010  2.017941e-012  3.979039e-013  1.193712e-012  2.160050e-012
            7.934489e-010  2.216893e-012  1.136868e-013  1.136868e-012  1.591616e-012
            7.488978e-010  2.160050e-012  2.842171e-013  5.684342e-013  3.069545e-012
            7.044179e-010  2.216893e-012  2.273737e-013  7.389644e-013  2.273737e-013
            6.599521e-010  2.501110e-012  2.842171e-013  9.663381e-013  3.410605e-013
            6.154011e-010  2.643219e-012  3.979039e-013  1.193712e-012  2.273737e-013
            5.709353e-010  2.643219e-012  3.410605e-013  7.958079e-013  4.547474e-013
          ];

ABSERR2 = [ % FINE-GRAIN OMP PARALLELISM with 3 threads for modified Talbot's method
            9.268177e-010  1.733724e-012  2.273737e-013  5.684342e-013  2.557954e-012
            8.823520e-010  1.875833e-012  1.136868e-013  7.389644e-013  2.444267e-012
            8.378152e-010  2.017941e-012  1.705303e-013  1.591616e-012  1.136868e-013
            7.934489e-010  2.188472e-012  1.136868e-013  7.389644e-013  6.821210e-013
            7.489120e-010  2.188472e-012  0.000000e+000  9.094947e-013  2.614797e-012
            7.044036e-010  2.245315e-012  2.842171e-013  3.410605e-013  2.273737e-013
            6.599663e-010  2.501110e-012  2.842171e-013  1.307399e-012  3.410605e-013
            6.154153e-010  2.643219e-012  3.979039e-013  8.526513e-013  1.591616e-012
            5.709353e-010  2.842171e-012  3.410605e-013  7.958079e-013  2.273737e-012
          ];

ABSERR3 = [ % NESTED COARSE/FINE-GRAIN OMP PARALLELISM with 3 (outer), 2 (inner) threads for modified Talbot's method
            9.269172e-010  1.733724e-012  2.273737e-013  5.684342e-013  4.831691e-012
            8.823520e-010  1.875833e-012  1.136868e-013  7.389644e-013  2.444267e-012
            8.378152e-010  2.017941e-012  1.705303e-013  8.526513e-013  1.023182e-012
            7.933494e-010  2.017941e-012  1.136868e-013  3.979039e-013  2.046363e-012
            7.488978e-010  2.160050e-012  2.842171e-013  1.307399e-012  3.410605e-013
            7.044179e-010  2.216893e-012  2.273737e-013  3.410605e-013  1.136868e-012
            6.599521e-010  2.501110e-012  2.842171e-013  9.663381e-013  5.684342e-013
            6.154011e-010  2.643219e-012  3.979039e-013  1.193712e-012  1.591616e-012
            5.709353e-010  2.842171e-012  3.410605e-013  7.958079e-013  1.818989e-012
          ];

PS_ERR1 = [ % COARSE-GRAIN OMP PARALLELISM with 3 threads for modified Talbot's method
            8.425616e-012  8.255830e-015  7.334635e-016  2.356922e-015  6.687461e-016
            7.931254e-012  8.072438e-015  3.652589e-016  9.675476e-016  2.112518e-015
            7.447246e-012  9.496195e-015  1.273293e-015  2.893847e-015  4.214732e-015
            6.975375e-012  1.037143e-014  3.623485e-016  2.747718e-015  3.098035e-015
            6.512155e-012  1.004674e-014  9.022765e-016  1.369721e-015  5.960281e-015
            6.059508e-012  1.025153e-014  7.189681e-016  1.775290e-015  4.404333e-016
            5.616614e-012  1.149936e-014  8.951720e-016  2.314582e-015  6.590541e-016
            5.182325e-012  1.208329e-014  1.248326e-015  2.850655e-015  4.383107e-016
            4.757794e-012  1.201463e-014  1.065814e-015  1.894781e-015  8.745141e-016
          ];

PS_ERR2 = [ % FINE-GRAIN OMP PARALLELISM with 3 threads for modified Talbot's method
            8.425616e-012  8.255830e-015  7.334635e-016  1.386425e-015  5.015596e-015
            7.931254e-012  8.879682e-015  3.652589e-016  1.796874e-015  4.780962e-015
            7.447246e-012  9.496195e-015  5.456968e-016  3.858462e-015  2.218280e-016
            6.975375e-012  1.023846e-014  3.623485e-016  1.786017e-015  1.327729e-015
            6.512279e-012  1.017894e-014  0.000000e+000  2.191553e-015  5.077276e-015
            6.059386e-012  1.038296e-014  8.987102e-016  8.193646e-016  4.404333e-016
            5.616735e-012  1.149936e-014  8.951720e-016  3.131494e-015  6.590541e-016
            5.182444e-012  1.208329e-014  1.248326e-015  2.036182e-015  3.068175e-015
            4.757794e-012  1.291896e-014  1.065814e-015  1.894781e-015  4.372571e-015
          ];

PS_ERR3 = [ % NESTED COARSE/FINE-GRAIN OMP PARALLELISM with 3 (outer), 2 (inner) threads for modified Talbot's method
            8.426520e-012  8.255830e-015  7.334635e-016  1.386425e-015  9.473903e-015
            7.931254e-012  8.879682e-015  3.652589e-016  1.796874e-015  4.780962e-015
            7.447246e-012  9.496195e-015  5.456968e-016  2.067033e-015  1.996452e-015
            6.974500e-012  9.440661e-015  3.623485e-016  9.617013e-016  3.983188e-015
            6.512155e-012  1.004674e-014  9.022765e-016  3.150358e-015  6.622534e-016
            6.059508e-012  1.025153e-014  7.189681e-016  8.193646e-016  2.202166e-015
            5.616614e-012  1.149936e-014  8.951720e-016  2.314582e-015  1.098424e-015
            5.182325e-012  1.208329e-014  1.248326e-015  2.850655e-015  3.068175e-015
            4.757794e-012  1.291896e-014  1.065814e-015  1.894781e-015  3.498057e-015
          ];

	      5 t in [100, 500],    9 x in [10, 20],    tol = 1.000000e-012
