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

               >>>   Example 1b - 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*sin(3*x)/6
			u(X0,t) = (X0+t)*sin(3*(X0+t))/6


	The analytical solution is

		u(x,t) = (x+t)*sin(3*(x+t))/6

	and its Laplace Transform is

		         (s*x+1)*sin(3*x)+3*x*cos(3*x)   s*cos(3*x)-3*sin(3*x)
		U(x,s) = ----------------------------- + ---------------------
		                   6*(s^2+9)                   (s^2+9)^2

	with double poles at +/-3i

	     and abscissa of convergence: sigma0 = 0

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

	   Ex. 1b: 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 3 threads for modified Talbot's method
            3.888302e-013  4.269073e-014  2.865261e-012  3.257043e-012  2.924215e-011
            7.776007e-014  5.833758e-014  1.098924e-013  4.562582e-012  7.555232e-012
            3.787104e-014  1.290774e-013  3.829830e-013  8.952484e-012  9.352681e-012
            7.285597e-015  1.480344e-014  5.788727e-013  1.980607e-012  1.054610e-011
            4.634010e-014  2.709868e-014  9.066476e-013  1.966222e-012  1.226057e-011
            1.429727e-012  4.002287e-014  2.835160e-011  3.218381e-012  3.940505e-011
            8.851054e-014  5.585515e-014  3.282203e-014  4.471152e-012  7.593039e-012
            4.085715e-014  1.049281e-013  3.615281e-013  7.686750e-012  9.652680e-012
            1.111478e-014  3.618232e-014  5.690028e-013  4.713101e-012  1.081505e-011
          ];

RELERR2 = [ % FINE-GRAIN OMP PARALLELISM with 3 threads for modified Talbot's method
            5.286261e-013  3.554157e-014  2.918509e-012  3.244538e-012  2.896327e-011
            1.017408e-013  1.126519e-014  1.024240e-013  4.451585e-012  7.640488e-012
            4.175525e-014  9.285242e-014  3.790245e-013  8.540260e-012  9.370498e-012
            0.000000e+000  1.245723e-013  5.722356e-013  1.568512e-012  1.046170e-011
            7.513229e-014  6.307037e-014  9.071139e-013  2.058667e-012  1.216111e-011
            1.981533e-012  4.081150e-014  2.903465e-011  3.212233e-012  3.893431e-011
            1.142756e-013  1.865851e-014  2.219963e-014  4.369039e-012  7.747474e-012
            4.728837e-014  4.507272e-014  3.588077e-013  7.305777e-012  9.613624e-012
            6.668870e-015  1.565439e-013  5.655710e-013  4.034484e-012  1.072271e-011
          ];

RELERR3 = [ % NESTED COARSE/FINE-GRAIN OMP PARALLELISM with 3 (outer), 2 (inner) threads for modified Talbot's method
            4.327452e-013  3.819697e-014  2.888387e-012  3.261420e-012  3.038085e-011
            8.712534e-014  2.507845e-014  1.069050e-013  4.544791e-012  7.345593e-012
            4.000736e-014  2.768918e-014  3.817106e-013  8.886696e-012  9.097829e-012
            5.261820e-015  8.323442e-014  5.762756e-013  1.908576e-012  1.024688e-011
            5.434740e-014  5.072009e-014  9.026844e-013  1.982249e-012  1.196919e-011
            1.584675e-012  4.002287e-014  2.834719e-011  3.220226e-012  3.992895e-011
            9.608849e-014  2.925173e-014  3.234462e-014  4.459589e-012  7.113427e-012
            4.331615e-014  2.463782e-015  3.641054e-013  7.653844e-012  9.206943e-012
            1.148528e-014  9.525548e-014  5.681792e-013  4.670449e-012  1.035770e-011
          ];

ABSERR1 = [ % COARSE-GRAIN OMP PARALLELISM with 3 threads for modified Talbot's method
            9.436896e-013  1.485034e-012  1.309530e-011  2.220730e-010  1.102682e-010
            9.734435e-013  1.545430e-012  3.659295e-012  2.441709e-010  3.910259e-010
            6.927792e-013  1.101341e-012  1.924860e-011  1.745271e-010  7.608918e-010
            1.278977e-013  1.882938e-013  2.850697e-011  4.308021e-011  8.629968e-010
            4.831691e-013  8.029133e-013  2.763301e-011  1.089617e-010  6.481997e-010
            9.199308e-013  1.442402e-012  1.640987e-011  2.231531e-010  1.869855e-010
            1.037392e-012  1.648459e-012  9.769963e-013  2.610321e-010  3.441087e-010
            7.673862e-013  1.286082e-012  1.794120e-011  2.025011e-010  7.656666e-010
            2.131628e-013  3.481659e-013  2.945200e-011  7.243095e-011  9.187602e-010
          ];

ABSERR2 = [ % FINE-GRAIN OMP PARALLELISM with 3 threads for modified Talbot's method
            1.282974e-012  1.236344e-012  1.333866e-011  2.212204e-010  1.092166e-010
            1.273648e-012  2.984279e-013  3.410605e-012  2.382308e-010  3.954383e-010
            7.638334e-013  7.922552e-013  1.904965e-011  1.664908e-010  7.623413e-010
            0.000000e+000  1.584510e-012  2.818012e-011  3.411671e-011  8.560903e-010
            7.833734e-013  1.868727e-012  2.764722e-011  1.140847e-010  6.429417e-010
            1.274980e-012  1.470823e-012  1.680522e-011  2.227267e-010  1.847518e-010
            1.339373e-012  5.506706e-013  6.608047e-013  2.550706e-010  3.511076e-010
            8.881784e-013  5.524470e-013  1.780620e-011  1.924647e-010  7.625687e-010
            1.278977e-013  1.506351e-012  2.927436e-011  6.200196e-011  9.109158e-010
          ];

ABSERR3 = [ % NESTED COARSE/FINE-GRAIN OMP PARALLELISM with 3 (outer), 2 (inner) threads for modified Talbot's method
            1.050271e-012  1.328715e-012  1.320100e-011  2.223715e-010  1.145621e-010
            1.090683e-012  6.643575e-013  3.559819e-012  2.432188e-010  3.801759e-010
            7.318590e-013  2.362555e-013  1.918465e-011  1.732445e-010  7.401582e-010
            9.237056e-014  1.058709e-012  2.837908e-011  4.151346e-011  8.385115e-010
            5.666578e-013  1.502798e-012  2.751221e-011  1.098499e-010  6.327951e-010
            1.019629e-012  1.442402e-012  1.640732e-011  2.232809e-010  1.894715e-010
            1.126210e-012  8.633094e-013  9.627854e-013  2.603571e-010  3.223732e-010
            8.135714e-013  3.019807e-014  1.806910e-011  2.016343e-010  7.303100e-010
            2.202682e-013  9.166001e-013  2.940936e-011  7.177547e-011  8.799077e-010
          ];

PS_ERR1 = [ % COARSE-GRAIN OMP PARALLELISM with 3 threads for modified Talbot's method
            3.888302e-013  4.269073e-014  2.865261e-012  3.257043e-012  2.924215e-011
            7.776007e-014  5.833758e-014  1.098924e-013  4.562582e-012  7.555232e-012
            3.787104e-014  1.290774e-013  3.829830e-013  8.952484e-012  9.352681e-012
            7.285597e-015  1.480344e-014  5.788727e-013  1.980607e-012  1.054610e-011
            4.634010e-014  2.709868e-014  9.066476e-013  1.966222e-012  1.226057e-011
            9.199308e-013  4.002287e-014  1.640987e-011  3.218381e-012  3.940505e-011
            8.851054e-014  5.585515e-014  3.282203e-014  4.471152e-012  7.593039e-012
            4.085715e-014  1.049281e-013  3.615281e-013  7.686750e-012  9.652680e-012
            1.111478e-014  3.618232e-014  5.690028e-013  4.713101e-012  1.081505e-011
          ];

PS_ERR2 = [ % FINE-GRAIN OMP PARALLELISM with 3 threads for modified Talbot's method
            5.286261e-013  3.554157e-014  2.918509e-012  3.244538e-012  2.896327e-011
            1.017408e-013  1.126519e-014  1.024240e-013  4.451585e-012  7.640488e-012
            4.175525e-014  9.285242e-014  3.790245e-013  8.540260e-012  9.370498e-012
            0.000000e+000  1.245723e-013  5.722356e-013  1.568512e-012  1.046170e-011
            7.513229e-014  6.307037e-014  9.071139e-013  2.058667e-012  1.216111e-011
            1.274980e-012  4.081150e-014  1.680522e-011  3.212233e-012  3.893431e-011
            1.142756e-013  1.865851e-014  2.219963e-014  4.369039e-012  7.747474e-012
            4.728837e-014  4.507272e-014  3.588077e-013  7.305777e-012  9.613624e-012
            6.668870e-015  1.565439e-013  5.655710e-013  4.034484e-012  1.072271e-011
          ];

PS_ERR3 = [ % NESTED COARSE/FINE-GRAIN OMP PARALLELISM with 3 (outer), 2 (inner) threads for modified Talbot's method
            4.327452e-013  3.819697e-014  2.888387e-012  3.261420e-012  3.038085e-011
            8.712534e-014  2.507845e-014  1.069050e-013  4.544791e-012  7.345593e-012
            4.000736e-014  2.768918e-014  3.817106e-013  8.886696e-012  9.097829e-012
            5.261820e-015  8.323442e-014  5.762756e-013  1.908576e-012  1.024688e-011
            5.434740e-014  5.072009e-014  9.026844e-013  1.982249e-012  1.196919e-011
            1.019629e-012  4.002287e-014  1.640732e-011  3.220226e-012  3.992895e-011
            9.608849e-014  2.925173e-014  3.234462e-014  4.459589e-012  7.113427e-012
            4.331615e-014  2.463782e-015  3.641054e-013  7.653844e-012  9.206943e-012
            1.148528e-014  9.525548e-014  5.681792e-013  4.670449e-012  1.035770e-011
          ];

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