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

               >>>   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 ./1SEQ/LTS2_ode/SEQ_main_ACCURACY.c

	LT samples computed by solving ODE problems by means of ode.c

	5 t in [100, 500],    9 x in [10, 20],    tol=1.000000e-008
====================================================================================


ABSERR1 = [ %  Tval(1)    Tval(2)    ...    Tval(5)
            2.493441e-010  5.409007e-010  3.072156e-010  6.144205e-010  7.084822e-011    % Xval( 1)
            5.277876e-008  5.009322e-008  7.373194e-007  4.180883e-006  4.321563e-005    % Xval( 2)
            2.273872e-008  2.523205e-007  1.476594e-006  9.367370e-007  1.044131e-004    % Xval( 3)
            8.310511e-009  1.297501e-007  3.426788e-006  2.261916e-005  7.943211e-005    % Xval( 4)
            2.526116e-008  4.453847e-007  6.499573e-006  4.575407e-006  8.927949e-005    % Xval( 5)
            4.140724e-009  4.974064e-007  3.670516e-006  8.357043e-006  4.721647e-005    % Xval( 6)
            8.664776e-009  2.809117e-007  1.570233e-006  6.458347e-005  2.547612e-004    % Xval( 7)
            2.360013e-008  1.501899e-008  2.379791e-006  3.027312e-005  1.531879e-004    % Xval( 8)
            3.319780e-008  6.785476e-007  7.415661e-006  3.236304e-005  4.271099e-005    % Xval( 9)
          ];

ABSERR2 = [ %  Tval(1)    Tval(2)    ...    Tval(5)
            2.882910e-008  1.633235e-007  3.232297e-008  3.599041e-010  2.498757e-011    % Xval( 1)
            7.137677e-007  1.757769e-006  1.557726e-007  4.991036e-008  3.599694e-007    % Xval( 2)
            2.142376e-006  1.829611e-006  3.979104e-006  3.995390e-007  3.262946e-006    % Xval( 3)
            8.355413e-008  2.680228e-008  4.617987e-006  3.884396e-006  2.712757e-006    % Xval( 4)
            5.385743e-006  3.772512e-006  8.332934e-007  6.687516e-006  8.177387e-007    % Xval( 5)
            1.347344e-005  2.835476e-006  4.050679e-006  6.475447e-007  3.234286e-007    % Xval( 6)
            2.175432e-005  2.057076e-006  7.963195e-006  8.169655e-006  5.920292e-006    % Xval( 7)
            1.587657e-005  3.591795e-006  3.960475e-006  1.711748e-005  9.443765e-006    % Xval( 8)
            2.640726e-006  2.776006e-006  6.848030e-007  1.978001e-005  5.752361e-006    % Xval( 9)
          ];

RELERR1 = [ %  Tval(1)    Tval(2)    ...    Tval(5)
            1.027377e-010  1.554944e-011  6.721898e-011  9.011423e-012  1.878831e-011    % Xval( 1)
            4.216043e-009  1.890940e-009  2.214246e-008  7.812406e-008  8.349937e-007    % Xval( 2)
            1.243021e-009  2.957200e-008  2.937930e-008  4.805056e-008  1.283418e-006    % Xval( 3)
            4.734021e-010  1.020080e-008  6.958556e-008  1.039913e-006  9.706860e-007    % Xval( 4)
            2.422765e-009  1.503193e-008  2.132530e-007  8.256354e-008  1.688704e-006    % Xval( 5)
            6.435381e-009  1.380172e-008  6.341610e-006  1.205278e-007  9.950328e-006    % Xval( 6)
            7.392805e-010  9.518200e-009  5.275173e-008  1.106234e-006  5.621512e-006    % Xval( 7)
            1.256517e-009  1.225360e-009  4.795449e-008  1.149139e-006  1.931224e-006    % Xval( 8)
            1.731007e-009  7.051644e-008  1.432681e-007  2.105871e-006  5.027659e-007    % Xval( 9)
          ];

RELERR2 = [ %  Tval(1)    Tval(2)    ...    Tval(5)
            1.187851e-008  4.695110e-009  7.072288e-009  5.278548e-012  6.626479e-012    % Xval( 1)
            5.701679e-008  6.635302e-008  4.678012e-009  9.326260e-010  6.955173e-009    % Xval( 2)
            1.171138e-007  2.144307e-007  7.917091e-008  2.049462e-008  4.010727e-008    % Xval( 3)
            4.759599e-009  2.107163e-009  9.377448e-008  1.785846e-007  3.315076e-008    % Xval( 4)
            5.165395e-007  1.273239e-007  2.734062e-008  1.206767e-007  1.546736e-008    % Xval( 5)
            2.093999e-005  7.867703e-008  6.998422e-006  9.339086e-009  6.815886e-008    % Xval( 6)
            1.856083e-006  6.970043e-008  2.675222e-007  1.399359e-007  1.306361e-007    % Xval( 7)
            8.452998e-007  2.930452e-007  7.980640e-008  6.497632e-007  1.190566e-007    % Xval( 8)
            1.376934e-007  2.884898e-007  1.323017e-008  1.287090e-006  6.771304e-008    % Xval( 9)
          ];

	      5 t in [100, 500],    9 x in [10, 20],    tol = 1.000000e-008
