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

               >>>   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/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 [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
            5.970224e-014  1.637579e-014  3.491651e-013  9.802159e-013  5.193401e-012
            9.842127e-014  1.397771e-013  1.324496e-013  5.085488e-012  2.385964e-011
            1.119660e-013  1.305622e-013  2.869927e-013  3.207767e-012  1.104206e-011
            1.372236e-013  1.778577e-013  5.698775e-013  4.154121e-012  3.011036e-012
            1.412204e-013  2.463585e-013  1.097455e-012  7.858936e-012  9.163281e-012
            1.401657e-013  2.496892e-013  1.211253e-012  8.841039e-012  1.255962e-011
            1.669775e-013  3.603784e-013  2.392753e-012  8.683276e-012  3.863032e-011
            1.398881e-013  3.411715e-013  1.242895e-012  8.431034e-013  4.521722e-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
            5.992429e-014  1.454392e-014  3.949618e-013  1.386224e-012  5.751788e-012
            9.842127e-014  1.381117e-013  1.875167e-013  5.695888e-012  2.546452e-011
            1.119105e-013  1.285638e-013  3.501643e-013  3.900102e-012  1.215850e-011
            1.366129e-013  1.764144e-013  4.989342e-013  5.010214e-012  1.265876e-012
            1.416645e-013  2.441380e-013  1.008305e-012  8.702927e-012  1.090783e-011
            1.402212e-013  2.465805e-013  1.122769e-012  9.672041e-012  1.486317e-011
            1.670331e-013  3.558265e-013  2.310374e-012  9.508616e-012  4.072420e-011
            1.398881e-013  3.411715e-013  1.161737e-012  1.680878e-012  4.793915e-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
            5.981327e-014  1.421085e-014  4.160006e-013  1.298406e-012  6.571133e-013
            9.858780e-014  1.375566e-013  2.300382e-013  5.707768e-012  1.646189e-011
            1.119660e-013  1.285638e-013  3.990142e-013  3.779754e-012  2.806866e-012
            1.367795e-013  1.749711e-013  4.305445e-013  4.890865e-012  1.271205e-011
            1.418310e-013  2.441380e-013  9.624523e-013  8.582912e-012  1.095846e-012
            1.399436e-013  2.459144e-013  1.085576e-012  9.539258e-012  3.347156e-012
            1.672551e-013  3.550493e-013  2.254197e-012  9.526491e-012  2.976680e-011
            1.401101e-013  3.380629e-013  1.104450e-012  1.818989e-012  3.300399e-011
          ];

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