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

               >>>   Example 2 - Talbot Suite DE   <<<

         Application of Talbot's method to solve the PDE equation

			u_tx (x,t) = exp(-x)*cos(t),         x>0,  t>0

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

	The analytical solution is

		u(x,t) = sin(t)*(1 - exp(-x))

	and its Laplace Transform is

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

	with simple poles at +/-i

	     and abscissa of convergence: sigma0 = 0

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

	   Ex. 2: output from ./2PAR/LTS1_fun/OMP_main_ACCURACY.c

	LT samples by means of a function

	      5 t in [100, 500],    9 x in [0, 5],    tol=1.000000e-012
====================================================================================


CHECK: NESTED PARALLELISM is not supported
                          Now it is supported

ABSERR1 = [ % COARSE-GRAIN OMP PARALLELISM with 4 threads for modified Talbot's method
            0.000000e+000  0.000000e+000  0.000000e+000  0.000000e+000  0.000000e+000
            5.070944e-014  1.854072e-014  6.977752e-014  2.784439e-013  4.425710e-012
            7.788215e-014  2.853273e-014  1.083578e-013  4.739542e-013  5.783818e-012
            9.253709e-014  3.075318e-014  1.358913e-013  6.610268e-013  7.971235e-012
            1.006972e-013  3.541611e-014  1.367795e-013  5.105916e-013  6.061540e-012
            1.048606e-013  3.652634e-014  1.564304e-013  5.133671e-013  7.278955e-012
            1.072475e-013  3.608225e-014  1.535438e-013  6.138423e-013  8.512413e-012
            1.079692e-013  3.796963e-014  1.525446e-013  6.774581e-013  9.526657e-012
            1.085798e-013  3.685940e-014  1.550982e-013  4.662937e-013  1.025208e-011
          ];

ABSERR2 = [ % FINE-GRAIN OMP PARALLELISM with 4 threads for modified Talbot's method
            0.000000e+000  0.000000e+000  0.000000e+000  0.000000e+000  0.000000e+000
            5.093148e-014  1.637579e-014  1.258993e-013  7.251977e-013  5.298040e-012
            7.788215e-014  2.520206e-014  1.736389e-013  1.034728e-012  6.900147e-012
            9.270362e-014  3.141931e-014  1.968425e-013  1.265099e-012  8.808398e-012
            1.004752e-013  3.186340e-014  2.255973e-013  1.290412e-012  8.225420e-012
            1.046385e-013  3.574918e-014  2.499112e-013  1.287970e-012  1.000061e-011
            1.070255e-013  3.230749e-014  2.272627e-013  1.425637e-012  1.067557e-011
            1.081912e-013  3.486100e-014  2.253753e-013  1.501244e-012  1.169020e-011
            1.090239e-013  3.608225e-014  2.530198e-013  1.460165e-012  1.185652e-011
          ];

ABSERR3 = [ % NESTED COARSE/FINE-GRAIN OMP PARALLELISM with 4 (outer), 2 (inner) threads for modified Talbot's method
            0.000000e+000  0.000000e+000  0.000000e+000  0.000000e+000  0.000000e+000
            5.082046e-014  1.637579e-014  1.432188e-013  6.690204e-013  7.965295e-013
            7.788215e-014  2.520206e-014  2.059464e-013  1.053047e-012  6.187828e-013
            9.264811e-014  2.942091e-014  2.493561e-013  1.258660e-012  6.428746e-013
            1.006972e-013  3.252953e-014  2.590150e-013  1.121103e-012  7.076006e-013
            1.050826e-013  3.508305e-014  2.939871e-013  1.194045e-012  8.576473e-013
            1.068590e-013  3.230749e-014  2.871037e-013  1.433076e-012  9.746648e-013
            1.081912e-013  3.641532e-014  2.726708e-013  1.444511e-012  1.849521e-012
            1.090239e-013  3.452794e-014  2.838840e-013  1.309952e-012  2.644218e-012
          ];

	      5 t in [100, 500],    9 x in [0, 5],    tol = 1.000000e-012
