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

               >>>   Example 3b - Talbot Suite DE   <<<

         Application of Talbot's method to solve the PDE equation

			u_t (x,t) = u_xx (x,t),         0 < x < L,  t>0

	with conditions:
			u(x,0+)   = x*(x-1)
			u(0,t) = 2*t
			u(L,t) = 2*t + L*(L-1)

	The analytical solution is

		u(x,t) = 2*t + x*(x-1)

	and its Laplace Transform is

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

	with a double pole at 0

	     and abscissa of convergence: sigma0 = 0

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

	   Ex. 3b: output from ./2PAR/LTS2_twpbvp/OMP_main_ACCURACY.c

	LT samples by solving ODE problems by means of twpbvp.f

	      5 t in [100, 500],    9 x in [0, 1],    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
            1.282757e-011  2.984279e-015  9.473903e-016  1.989520e-015  6.821210e-016
            1.285421e-011  2.842948e-015  3.790252e-016  1.279152e-015  4.547971e-016
            1.287346e-011  2.132628e-015  3.790746e-016  7.107093e-016  5.685408e-016
            1.288502e-011  2.417262e-015  5.686563e-016  9.950513e-016  2.274270e-016
            1.288816e-011  2.701751e-015  7.582282e-016  5.686119e-016  5.685763e-016
            1.288502e-011  2.417262e-015  5.686563e-016  9.950513e-016  3.411405e-015
            1.287346e-011  2.132628e-015  3.790746e-016  1.563560e-015  5.685408e-016
            1.285435e-011  2.842948e-015  1.326588e-015  4.263839e-016  3.410978e-016
            1.282771e-011  2.984279e-015  9.473903e-016  2.842171e-016  2.842171e-015
          ];

RELERR2 = [ % FINE-GRAIN OMP PARALLELISM with 4 threads for modified Talbot's method
            1.282757e-011  2.984279e-015  0.000000e+000  1.989520e-015  2.387424e-015
            1.285421e-011  2.842948e-015  3.790252e-016  2.274048e-015  4.889069e-015
            1.287346e-011  2.132628e-015  3.790746e-016  1.563560e-015  3.752369e-015
            1.288502e-011  2.417262e-015  5.686563e-016  1.847953e-015  3.752545e-015
            1.288816e-011  2.843948e-015  7.582282e-016  2.274448e-015  5.913194e-015
            1.288502e-011  2.417262e-015  5.686563e-016  1.847953e-015  6.822809e-016
            1.287346e-011  2.132628e-015  3.790746e-016  1.563560e-015  3.752369e-015
            1.285421e-011  2.842948e-015  3.790252e-016  2.274048e-015  4.547971e-016
            1.282757e-011  1.989520e-015  9.473903e-016  1.989520e-015  2.387424e-015
          ];

RELERR3 = [ % NESTED COARSE/FINE-GRAIN OMP PARALLELISM with 4 (outer), 2 (inner) threads for modified Talbot's method
            1.282757e-011  2.984279e-015  0.000000e+000  2.842171e-015  5.115908e-015
            1.285421e-011  2.842948e-015  3.790252e-016  2.274048e-015  3.979475e-015
            1.287346e-011  2.985679e-015  3.790746e-016  1.563560e-015  3.866077e-015
            1.288502e-011  2.417262e-015  5.686563e-016  1.421502e-016  2.842837e-015
            1.288816e-011  2.701751e-015  7.582282e-016  1.421530e-015  5.913194e-015
            1.288502e-011  2.417262e-015  5.686563e-016  1.421502e-016  6.822809e-016
            1.287346e-011  2.985679e-015  3.790746e-016  1.563560e-015  3.866077e-015
            1.285435e-011  2.842948e-015  3.790252e-016  4.263839e-016  4.889069e-015
            1.282771e-011  2.984279e-015  9.473903e-016  2.842171e-015  6.821210e-016
          ];

	      5 t in [100, 500],    9 x in [0, 1],    tol = 1.000000e-012
