MAIN_accuracy

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

               >>>   Example 5 - Talbot Suite DE   <<<

         Application of Talbot's method to solve the PDE equation

			u_t (x,y,t) = u_xx (x,y,t) + u_yy (x,y,t),      0 < x,y < 1,  t>0

	with conditions:
			u(x,y,0+) = x*(x-1) + y*(y-1)
			u(0,y,t) = u(1,y,t) = 4*t + y*(y-1)
			u(x,0,t) = u(x,1,t) = 4*t + x*(x-1)

	The analytical solution is

		u(x,y,t) = 4*t + x*(x-1) + y*(y-1)

	and its Laplace Transform is

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

	with a double pole at 0

	     and abscissa of convergence: sigma0 = 0

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

NTval = 5  t in [100, 500],  NXYval = 9,  x,y in [0, 1],  tol = 1.000000e-12

    num (x,y)   Relative Error in Inverse Laplace Transform u(h,k) = u(X(h),Y(h),t(k)):
            1   1.2854e-11   2.7008e-15   3.7903e-16   2.9847e-15   1.0119e-14
            2   1.2863e-11   2.7011e-15   1.7057e-15   5.4011e-15   1.7738e-14
            3   1.2869e-11   3.2699e-15   2.2744e-15   6.9648e-15   2.0808e-14
            4   1.2871e-11   2.9856e-15   1.1372e-15    7.107e-15   2.0467e-14
            5   1.2869e-11   3.2699e-15   2.2744e-15   6.9648e-15   2.0808e-14
            6   1.2863e-11   2.7011e-15   1.7057e-15   4.4062e-15   1.6032e-14
            7   1.2854e-11   2.7008e-15   3.7903e-16   4.8324e-15   1.3644e-14
            8   1.2863e-11   2.7011e-15   1.7057e-15   6.2539e-15   1.6942e-14
            9   1.2873e-11   2.9857e-15   2.0849e-15   7.6757e-15    2.729e-14
           10   1.2879e-11   3.4124e-15   3.2223e-15   9.8081e-15   3.6729e-14
           11    1.288e-11   3.6968e-15   2.2746e-15   9.8082e-15   3.7639e-14
           12   1.2879e-11   3.4124e-15   3.2223e-15   8.8131e-15      3.4e-14
           13   1.2873e-11   2.9857e-15   2.0849e-15   9.5235e-15   3.0815e-14
           14   1.2863e-11   2.7011e-15   1.7057e-15   6.2539e-15   1.6032e-14
           15   1.2869e-11   3.2699e-15   1.3267e-15   6.9648e-15   2.2628e-14
           16   1.2879e-11   3.4124e-15   2.2745e-15   9.8081e-15   3.3204e-14
           17   1.2884e-11   3.2704e-15   3.0328e-15   1.0661e-14    3.798e-14
           18   1.2886e-11   3.5549e-15   3.0329e-15   1.0519e-14   3.6275e-14
           19   1.2884e-11   4.1236e-15   3.0328e-15   1.0661e-14   3.5365e-14
           20   1.2879e-11   3.4124e-15   2.2745e-15   7.9602e-15   3.2294e-14
           21   1.2869e-11   3.2699e-15   2.2744e-15   7.8176e-15   2.3424e-14
           22   1.2872e-11   2.9856e-15   2.0849e-15   5.4013e-15   2.1377e-14
           23    1.288e-11   2.8437e-15   2.2746e-15   8.8131e-15   3.2294e-14
           24   1.2886e-11   3.5549e-15   3.0329e-15   1.0519e-14   3.9004e-14
           25   1.2888e-11   3.5549e-15   3.2225e-15   1.1088e-14   3.8436e-14
           26   1.2886e-11   3.5549e-15   3.0329e-15   1.0519e-14    3.184e-14
           27    1.288e-11   2.8437e-15   2.2746e-15   8.8131e-15   2.9679e-14
           28   1.2872e-11   2.9856e-15   1.1372e-15   5.4013e-15   2.1377e-14
           29   1.2869e-11   3.2699e-15   1.3267e-15   5.2591e-15   2.2628e-14
           30   1.2879e-11   3.4124e-15   2.2745e-15   8.8131e-15      3.4e-14
           31   1.2884e-11   4.1236e-15   3.0328e-15   1.0661e-14   3.5365e-14
           32   1.2886e-11   3.5549e-15   3.0329e-15   1.0519e-14   3.5365e-14
           33   1.2884e-11   4.1236e-15   3.0328e-15   9.6662e-15   3.5365e-14
           34   1.2879e-11   3.4124e-15   2.2745e-15   9.8081e-15      3.4e-14
           35   1.2869e-11   3.2699e-15   1.3267e-15    6.112e-15   2.2628e-14
           36   1.2863e-11   2.7011e-15   1.7057e-15   5.4011e-15   1.7738e-14
           37   1.2873e-11   2.9857e-15   2.0849e-15   6.8228e-15    2.729e-14
           38   1.2879e-11   3.4124e-15   3.2223e-15   7.9602e-15   3.2294e-14
           39    1.288e-11   3.6968e-15   2.2746e-15   7.9603e-15   3.0588e-14
           40   1.2879e-11   3.4124e-15   2.2745e-15   7.9602e-15   2.8655e-14
           41   1.2873e-11   2.9857e-15   2.0849e-15   8.5285e-15   2.6267e-14
           42   1.2863e-11   2.7011e-15    7.581e-16   4.4062e-15   1.7738e-14
           43   1.2854e-11   2.7008e-15   3.7903e-16   2.1319e-15   1.0119e-14
           44   1.2863e-11   2.7011e-15    7.581e-16   4.4062e-15   1.6942e-14
           45   1.2869e-11   3.2699e-15   1.3267e-15   4.2642e-15   2.3424e-14
           46   1.2871e-11   2.9856e-15   1.1372e-15   3.5535e-15   1.9671e-14
           47   1.2869e-11   3.2699e-15   1.3267e-15   5.2591e-15   2.0808e-14
           48   1.2863e-11   2.7011e-15   1.7057e-15   5.4011e-15   1.7738e-14
           49   1.2854e-11   2.7008e-15   3.7903e-16   4.8324e-15   1.4554e-14
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