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

               >>>   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/LTS1_fun/OMP_main_ACCURACY.c

	LT samples by means of a function

	      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 4 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  1.796874e-015  4.780962e-015
            7.448130e-012  9.496195e-015  5.456968e-016  2.067033e-015  3.327420e-015
            6.974500e-012  1.037143e-014  1.449394e-015  1.923403e-015  1.327729e-015
            6.512155e-012  1.097210e-014  9.022765e-016  2.191553e-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  5.446076e-016  1.098424e-015
            5.182325e-012  1.208329e-014  1.248326e-015  2.036182e-015  2.191553e-015
            4.757794e-012  1.291896e-014  1.065814e-015  1.894781e-015  4.372571e-015
          ];

RELERR2 = [ % FINE-GRAIN OMP PARALLELISM with 4 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  1.796874e-015  4.780962e-015
            7.448130e-012  9.496195e-015  5.456968e-016  2.067033e-015  1.109140e-015
            6.974500e-012  9.440661e-015  3.623485e-016  2.747718e-015  4.868341e-015
            6.512279e-012  1.017894e-014  9.022765e-016  2.191553e-015  4.635774e-015
            6.059386e-012  1.038296e-014  8.987102e-016  2.594655e-015  6.606499e-015
            5.616735e-012  1.149936e-014  8.951720e-016  2.314582e-015  2.416532e-015
            5.182444e-012  1.208329e-014  1.248326e-015  2.850655e-015  3.068175e-015
            4.757794e-012  1.201463e-014  1.776357e-016  2.842171e-015  2.623542e-015
          ];

RELERR3 = [ % NESTED COARSE/FINE-GRAIN OMP PARALLELISM with 4 (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  5.670444e-015
            7.447246e-012  9.496195e-015  5.456968e-016  1.240220e-015  1.996452e-015
            6.975375e-012  9.440661e-015  3.623485e-016  1.373859e-016  4.425765e-016
            6.512155e-012  1.097210e-014  9.022765e-016  4.109163e-016  1.986760e-015
            6.059508e-012  1.025153e-014  7.189681e-016  8.193646e-016  4.844766e-015
            5.616614e-012  1.149936e-014  8.951720e-016  5.446076e-016  3.295271e-015
            5.182325e-012  1.208329e-014  3.566646e-016  2.036182e-015  4.821418e-015
            4.757794e-012  1.291896e-014  1.065814e-015  9.473903e-016  8.745141e-015
          ];

ABSERR1 = [ % COARSE-GRAIN OMP PARALLELISM with 4 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  7.389644e-013  2.444267e-012
            8.379146e-010  2.017941e-012  1.705303e-013  8.526513e-013  1.705303e-012
            7.933494e-010  2.216893e-012  4.547474e-013  7.958079e-013  6.821210e-013
            7.488978e-010  2.359002e-012  2.842171e-013  9.094947e-013  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  2.273737e-013  5.684342e-013
            6.154011e-010  2.643219e-012  3.979039e-013  8.526513e-013  1.136868e-012
            5.709353e-010  2.842171e-012  3.410605e-013  7.958079e-013  2.273737e-012
          ];

ABSERR2 = [ % FINE-GRAIN OMP PARALLELISM with 4 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  7.389644e-013  2.444267e-012
            8.379146e-010  2.017941e-012  1.705303e-013  8.526513e-013  5.684342e-013
            7.933494e-010  2.017941e-012  1.136868e-013  1.136868e-012  2.501110e-012
            7.489120e-010  2.188472e-012  2.842171e-013  9.094947e-013  2.387424e-012
            7.044036e-010  2.245315e-012  2.842171e-013  1.080025e-012  3.410605e-012
            6.599663e-010  2.501110e-012  2.842171e-013  9.663381e-013  1.250555e-012
            6.154153e-010  2.643219e-012  3.979039e-013  1.193712e-012  1.591616e-012
            5.709353e-010  2.643219e-012  5.684342e-014  1.193712e-012  1.364242e-012
          ];

ABSERR3 = [ % NESTED COARSE/FINE-GRAIN OMP PARALLELISM with 4 (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  2.899014e-012
            8.378152e-010  2.017941e-012  1.705303e-013  5.115908e-013  1.023182e-012
            7.934489e-010  2.017941e-012  1.136868e-013  5.684342e-014  2.273737e-013
            7.488978e-010  2.359002e-012  2.842171e-013  1.705303e-013  1.023182e-012
            7.044179e-010  2.216893e-012  2.273737e-013  3.410605e-013  2.501110e-012
            6.599521e-010  2.501110e-012  2.842171e-013  2.273737e-013  1.705303e-012
            6.154011e-010  2.643219e-012  1.136868e-013  8.526513e-013  2.501110e-012
            5.709353e-010  2.842171e-012  3.410605e-013  3.979039e-013  4.547474e-012
          ];

PS_ERR1 = [ % COARSE-GRAIN OMP PARALLELISM with 4 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  1.796874e-015  4.780962e-015
            7.448130e-012  9.496195e-015  5.456968e-016  2.067033e-015  3.327420e-015
            6.974500e-012  1.037143e-014  1.449394e-015  1.923403e-015  1.327729e-015
            6.512155e-012  1.097210e-014  9.022765e-016  2.191553e-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  5.446076e-016  1.098424e-015
            5.182325e-012  1.208329e-014  1.248326e-015  2.036182e-015  2.191553e-015
            4.757794e-012  1.291896e-014  1.065814e-015  1.894781e-015  4.372571e-015
          ];

PS_ERR2 = [ % FINE-GRAIN OMP PARALLELISM with 4 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  1.796874e-015  4.780962e-015
            7.448130e-012  9.496195e-015  5.456968e-016  2.067033e-015  1.109140e-015
            6.974500e-012  9.440661e-015  3.623485e-016  2.747718e-015  4.868341e-015
            6.512279e-012  1.017894e-014  9.022765e-016  2.191553e-015  4.635774e-015
            6.059386e-012  1.038296e-014  8.987102e-016  2.594655e-015  6.606499e-015
            5.616735e-012  1.149936e-014  8.951720e-016  2.314582e-015  2.416532e-015
            5.182444e-012  1.208329e-014  1.248326e-015  2.850655e-015  3.068175e-015
            4.757794e-012  1.201463e-014  1.776357e-016  2.842171e-015  2.623542e-015
          ];

PS_ERR3 = [ % NESTED COARSE/FINE-GRAIN OMP PARALLELISM with 4 (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  5.670444e-015
            7.447246e-012  9.496195e-015  5.456968e-016  1.240220e-015  1.996452e-015
            6.975375e-012  9.440661e-015  3.623485e-016  1.373859e-016  4.425765e-016
            6.512155e-012  1.097210e-014  9.022765e-016  4.109163e-016  1.986760e-015
            6.059508e-012  1.025153e-014  7.189681e-016  8.193646e-016  4.844766e-015
            5.616614e-012  1.149936e-014  8.951720e-016  5.446076e-016  3.295271e-015
            5.182325e-012  1.208329e-014  3.566646e-016  2.036182e-015  4.821418e-015
            4.757794e-012  1.291896e-014  1.065814e-015  9.473903e-016  8.745141e-015
          ];

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