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

               >>>   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/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
            3.888302e-013  4.269073e-014  2.865261e-012  3.257043e-012  2.924215e-011
            8.230081e-014  8.502534e-014  2.865524e-012  3.287412e-011  7.399739e-011
            5.282525e-014  2.273011e-012  1.265441e-012  2.066663e-010  1.607631e-010
            2.086514e-013  2.054605e-012  3.794704e-014  1.178389e-010  2.299243e-010
            5.615330e-013  3.112751e-013  2.228036e-012  2.988568e-011  3.106424e-010
            2.341295e-012  1.989314e-013  8.583605e-010  3.681801e-011  3.304658e-009
            1.879333e-014  3.539098e-014  9.718901e-012  3.796895e-012  5.201456e-011
            2.275516e-013  4.126835e-012  1.438524e-012  7.585795e-011  5.913349e-010
            3.721600e-013  9.384142e-012  1.094078e-013  7.910069e-011  1.099697e-009
          ];

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
            1.023084e-013  1.334388e-013  2.873846e-012  3.277547e-011  7.385530e-011
            4.796998e-014  2.488695e-012  1.261907e-012  2.061814e-010  1.607490e-010
            2.167465e-013  2.197612e-012  3.837990e-014  1.174322e-010  2.298490e-010
            5.899844e-013  3.513236e-013  2.228152e-012  2.977541e-011  3.105393e-010
            2.888960e-012  2.007058e-013  8.581589e-010  3.680571e-011  3.305493e-009
            4.501306e-014  2.768682e-015  9.710427e-012  3.906066e-012  5.195765e-011
            2.201746e-013  4.280894e-012  1.429074e-012  7.548224e-011  5.912480e-010
            3.784584e-013  9.578345e-012  1.139378e-013  7.843629e-011  1.099666e-009
          ];

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
            8.755103e-014  1.178821e-013  2.864031e-012  3.286708e-011  7.425852e-011
            5.049472e-014  2.424364e-012  1.284951e-012  2.067462e-010  1.622828e-010
            2.112823e-013  2.166050e-012  2.250851e-014  1.175227e-010  2.363540e-010
            5.770365e-013  3.615155e-013  2.472008e-012  2.666151e-011  3.113582e-010
            2.603739e-012  2.109580e-013  8.830093e-010  3.628247e-011  3.777217e-009
            2.712909e-014  2.804795e-014  9.928962e-012  6.262436e-012  3.532255e-012
            2.317130e-013  4.221328e-012  1.451696e-012  6.753751e-011  6.008688e-010
            3.832748e-013  9.359405e-012  3.434608e-013  7.827909e-011  1.106236e-009
          ];

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
            1.030287e-012  2.252420e-012  9.541878e-011  1.759290e-009  3.829783e-009
            9.663381e-013  1.939426e-011  6.360068e-011  4.028923e-009  1.307896e-008
            3.662848e-012  2.613376e-011  1.868727e-012  2.563116e-009  1.881492e-008
            5.854872e-012  9.222845e-012  6.790657e-011  1.656169e-009  1.642324e-008
            1.506462e-012  7.169376e-012  4.968180e-010  2.552852e-009  1.568132e-008
            2.202682e-013  1.044498e-012  2.892975e-010  2.216680e-010  2.357247e-009
            4.273915e-012  5.058176e-011  7.138823e-011  1.998416e-009  4.690567e-008
            7.137402e-012  9.029932e-011  5.663026e-012  1.215620e-009  9.342151e-008
          ];

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
            1.280753e-012  3.534950e-012  9.569590e-011  1.754010e-009  3.822429e-009
            8.775203e-013  2.123457e-011  6.342304e-011  4.019469e-009  1.307781e-008
            3.804956e-012  2.795275e-011  1.890044e-012  2.554270e-009  1.880875e-008
            6.151524e-012  1.040945e-011  6.791012e-011  1.650058e-009  1.641779e-008
            1.858846e-012  7.233325e-012  4.967013e-010  2.552000e-009  1.568528e-008
            5.275780e-013  8.171241e-014  2.890452e-010  2.280416e-010  2.354668e-009
            4.135359e-012  5.247003e-011  7.091927e-011  1.988518e-009  4.689878e-008
            7.258194e-012  9.216805e-011  5.897505e-012  1.205409e-009  9.341886e-008
          ];

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
            1.096012e-012  3.122835e-012  9.536905e-011  1.758913e-009  3.843297e-009
            9.237056e-013  2.068568e-011  6.458123e-011  4.030479e-009  1.320259e-008
            3.709033e-012  2.755129e-011  1.108447e-012  2.556238e-009  1.934106e-008
            6.016521e-012  1.071143e-011  7.534240e-011  1.477495e-009  1.646109e-008
            1.675327e-012  7.602807e-012  5.110847e-010  2.515719e-009  1.792371e-008
            3.179679e-013  8.277823e-013  2.955503e-010  3.656098e-010  1.600782e-010
            4.352074e-012  5.173995e-011  7.204193e-011  1.779220e-009  4.766191e-008
            7.350565e-012  9.006129e-011  1.777778e-011  1.202993e-009  9.397698e-008
          ];

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
            8.230081e-014  8.502534e-014  2.865524e-012  3.287412e-011  7.399739e-011
            5.282525e-014  2.273011e-012  1.265441e-012  2.066663e-010  1.607631e-010
            2.086514e-013  2.054605e-012  3.794704e-014  1.178389e-010  2.299243e-010
            5.615330e-013  3.112751e-013  2.228036e-012  2.988568e-011  3.106424e-010
            1.506462e-012  1.989314e-013  4.968180e-010  3.681801e-011  3.304658e-009
            1.879333e-014  3.539098e-014  9.718901e-012  3.796895e-012  5.201456e-011
            2.275516e-013  4.126835e-012  1.438524e-012  7.585795e-011  5.913349e-010
            3.721600e-013  9.384142e-012  1.094078e-013  7.910069e-011  1.099697e-009
          ];

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
            1.023084e-013  1.334388e-013  2.873846e-012  3.277547e-011  7.385530e-011
            4.796998e-014  2.488695e-012  1.261907e-012  2.061814e-010  1.607490e-010
            2.167465e-013  2.197612e-012  3.837990e-014  1.174322e-010  2.298490e-010
            5.899844e-013  3.513236e-013  2.228152e-012  2.977541e-011  3.105393e-010
            1.858846e-012  2.007058e-013  4.967013e-010  3.680571e-011  3.305493e-009
            4.501306e-014  2.768682e-015  9.710427e-012  3.906066e-012  5.195765e-011
            2.201746e-013  4.280894e-012  1.429074e-012  7.548224e-011  5.912480e-010
            3.784584e-013  9.578345e-012  1.139378e-013  7.843629e-011  1.099666e-009
          ];

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
            8.755103e-014  1.178821e-013  2.864031e-012  3.286708e-011  7.425852e-011
            5.049472e-014  2.424364e-012  1.284951e-012  2.067462e-010  1.622828e-010
            2.112823e-013  2.166050e-012  2.250851e-014  1.175227e-010  2.363540e-010
            5.770365e-013  3.615155e-013  2.472008e-012  2.666151e-011  3.113582e-010
            1.675327e-012  2.109580e-013  5.110847e-010  3.628247e-011  3.777217e-009
            2.712909e-014  2.804795e-014  9.928962e-012  6.262436e-012  3.532255e-012
            2.317130e-013  4.221328e-012  1.451696e-012  6.753751e-011  6.008688e-010
            3.832748e-013  9.359405e-012  3.434608e-013  7.827909e-011  1.106236e-009
          ];

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