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

               >>>   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,y,s) = --- + -----------------
		           s^2           s

	with a double pole at 0

	     and abscissa of convergence: sigma0 = 0

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

	   Ex. 5: output from ./2PAR/LTS1_fun/OMP_main_ACCURACY.c

	LT samples by a function

	      5 t in [100, 500],    9 x,y 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          1.285435e-011  2.700801e-015  3.790252e-016  1.279152e-015  3.410978e-016
 2          1.286341e-011  2.843226e-015  1.895250e-016  2.700563e-015  2.615185e-015
 3          1.286904e-011  3.269902e-015  3.790647e-016  1.705669e-015  1.364477e-015
 4          1.287168e-011  2.985621e-015  1.895348e-016  1.705686e-015  1.137073e-016
 5          1.286904e-011  3.269902e-015  3.790647e-016  1.705669e-015  1.364477e-015
 6          1.286341e-011  2.843226e-015  1.895250e-016  2.700563e-015  2.615185e-015
 7          1.285435e-011  2.700801e-015  3.790252e-016  1.279152e-015  3.410978e-016
 8          1.286341e-011  2.843226e-015  1.895250e-016  2.700563e-015  2.615185e-015
 9          1.287360e-011  2.985679e-015  3.790746e-016  2.416412e-015  1.250790e-015
10          1.287895e-011  2.417120e-015  5.686341e-016  9.950222e-016  5.685541e-016
11          1.288117e-011  2.843726e-015  5.686415e-016  2.700801e-015  1.250829e-015
12          1.287895e-011  2.417120e-015  5.686341e-016  9.950222e-016  5.685541e-016
13          1.287360e-011  2.985679e-015  3.790746e-016  2.274270e-015  3.411245e-016
14          1.286341e-011  2.701065e-015  7.580998e-016  2.700563e-015  1.819259e-015
15          1.286890e-011  3.269902e-015  1.326726e-015  1.705669e-015  4.548255e-016
16          1.287895e-011  2.417120e-015  5.686341e-016  1.705752e-015  5.685541e-016
17          1.288502e-011  2.275070e-015  3.791042e-016  8.529012e-016  2.274270e-016
18          1.288609e-011  2.701698e-015  3.791092e-016  2.558728e-015  6.822863e-016
19          1.288502e-011  2.275070e-015  3.791042e-016  8.529012e-016  2.274270e-016
20          1.287895e-011  2.417120e-015  5.686341e-016  1.705752e-015  5.685541e-016
21          1.286890e-011  3.269902e-015  1.326726e-015  1.705669e-015  4.548255e-016
22          1.287154e-011  2.985621e-015  3.790696e-016  8.528428e-016  9.096582e-016
23          1.288131e-011  2.843726e-015  5.686415e-016  2.700801e-015  1.250829e-015
24          1.288609e-011  2.701698e-015  3.791092e-016  2.558728e-015  6.822863e-016
25          1.288816e-011  2.701751e-015  1.516456e-015  1.421530e-015  5.685763e-016
26          1.288609e-011  2.701698e-015  3.791092e-016  2.558728e-015  6.822863e-016
27          1.288131e-011  2.843726e-015  5.686415e-016  2.700801e-015  1.250829e-015
28          1.287154e-011  2.985621e-015  3.790696e-016  8.528428e-016  9.096582e-016
29          1.286890e-011  3.269902e-015  1.326726e-015  1.705669e-015  4.548255e-016
30          1.287895e-011  2.417120e-015  5.686341e-016  1.705752e-015  5.685541e-016
31          1.288502e-011  2.275070e-015  3.791042e-016  8.529012e-016  2.274270e-016
32          1.288609e-011  2.701698e-015  3.791092e-016  2.558728e-015  6.822863e-016
33          1.288502e-011  2.275070e-015  3.791042e-016  8.529012e-016  2.274270e-016
34          1.287895e-011  2.417120e-015  5.686341e-016  1.705752e-015  5.685541e-016
35          1.286890e-011  3.269902e-015  1.326726e-015  1.705669e-015  4.548255e-016
36          1.286341e-011  2.701065e-015  7.580998e-016  2.700563e-015  1.819259e-015
37          1.287360e-011  2.985679e-015  3.790746e-016  2.274270e-015  3.411245e-016
38          1.287895e-011  2.417120e-015  5.686341e-016  1.705752e-015  5.685541e-016
39          1.288131e-011  2.843726e-015  5.686415e-016  2.700801e-015  1.250829e-015
40          1.287895e-011  2.417120e-015  5.686341e-016  1.705752e-015  5.685541e-016
41          1.287360e-011  2.985679e-015  3.790746e-016  2.274270e-015  3.411245e-016
42          1.286341e-011  2.701065e-015  7.580998e-016  2.700563e-015  1.819259e-015
43          1.285435e-011  2.700801e-015  1.137076e-015  1.279152e-015  2.160286e-015
44          1.286341e-011  2.701065e-015  7.580998e-016  2.700563e-015  1.819259e-015
45          1.286890e-011  3.269902e-015  1.326726e-015  1.705669e-015  4.548255e-016
46          1.287154e-011  2.985621e-015  3.790696e-016  8.528428e-016  9.096582e-016
47          1.286890e-011  3.269902e-015  1.326726e-015  1.705669e-015  4.548255e-016
48          1.286341e-011  2.701065e-015  7.580998e-016  2.700563e-015  1.819259e-015
49          1.285435e-011  2.700801e-015  1.137076e-015  1.279152e-015  2.160286e-015
          ];

RELERR2 = [ % FINE-GRAIN OMP PARALLELISM with 4 threads for modified Talbot's method
 1          1.285435e-011  2.700801e-015  3.790252e-016  2.131920e-015  2.273985e-015
 2          1.286341e-011  2.843226e-015  7.580998e-016  2.700563e-015  0.000000e+000
 3          1.286904e-011  2.416884e-015  1.326726e-015  2.558504e-015  2.274128e-015
 4          1.287168e-011  2.132586e-015  1.895348e-016  2.700669e-015  2.501560e-015
 5          1.286904e-011  2.416884e-015  1.326726e-015  2.558504e-015  2.274128e-015
 6          1.286341e-011  2.843226e-015  7.580998e-016  2.700563e-015  0.000000e+000
 7          1.285435e-011  2.700801e-015  3.790252e-016  2.131920e-015  2.273985e-015
 8          1.286341e-011  2.843226e-015  7.580998e-016  2.700563e-015  0.000000e+000
 9          1.287360e-011  2.985679e-015  3.790746e-016  5.685674e-016  5.685408e-015
10          1.287895e-011  2.417120e-015  5.686341e-016  2.700775e-015  5.685541e-016
11          1.288117e-011  2.843726e-015  5.686415e-016  2.700801e-015  2.387946e-015
12          1.287895e-011  2.417120e-015  5.686341e-016  2.700775e-015  5.685541e-016
13          1.287360e-011  2.985679e-015  3.790746e-016  5.685674e-016  5.685408e-015
14          1.286341e-011  2.843226e-015  7.580998e-016  2.700563e-015  0.000000e+000
15          1.286904e-011  2.416884e-015  1.326726e-015  2.558504e-015  2.274128e-015
16          1.287895e-011  2.417120e-015  5.686341e-016  2.700775e-015  5.685541e-016
17          1.288502e-011  2.275070e-015  3.791042e-016  1.705802e-015  1.137135e-015
18          1.288609e-011  2.701698e-015  3.791092e-016  1.563667e-015  1.137144e-016
19          1.288502e-011  2.275070e-015  3.791042e-016  1.705802e-015  1.137135e-015
20          1.287895e-011  2.417120e-015  5.686341e-016  2.700775e-015  5.685541e-016
21          1.286904e-011  2.416884e-015  1.326726e-015  2.558504e-015  2.274128e-015
22          1.287168e-011  2.132586e-015  1.895348e-016  2.700669e-015  2.501560e-015
23          1.288117e-011  2.843726e-015  5.686415e-016  2.700801e-015  2.387946e-015
24          1.288609e-011  2.701698e-015  3.791092e-016  1.563667e-015  1.137144e-016
25          1.288816e-011  2.701751e-015  5.686711e-016  2.132295e-015  6.026909e-015
26          1.288609e-011  2.701698e-015  3.791092e-016  1.563667e-015  1.137144e-016
27          1.288117e-011  2.843726e-015  5.686415e-016  2.700801e-015  2.387946e-015
28          1.287168e-011  2.132586e-015  1.895348e-016  2.700669e-015  2.501560e-015
29          1.286904e-011  2.416884e-015  1.326726e-015  2.558504e-015  2.274128e-015
30          1.287895e-011  2.417120e-015  5.686341e-016  2.700775e-015  5.685541e-016
31          1.288502e-011  2.275070e-015  3.791042e-016  1.705802e-015  1.137135e-015
32          1.288609e-011  2.701698e-015  3.791092e-016  1.563667e-015  1.137144e-016
33          1.288502e-011  2.275070e-015  3.791042e-016  1.705802e-015  1.137135e-015
34          1.287895e-011  2.417120e-015  5.686341e-016  2.700775e-015  5.685541e-016
35          1.286904e-011  2.416884e-015  1.326726e-015  2.558504e-015  2.274128e-015
36          1.286341e-011  2.843226e-015  7.580998e-016  2.700563e-015  0.000000e+000
37          1.287360e-011  2.985679e-015  3.790746e-016  1.421419e-015  5.685408e-015
38          1.287895e-011  2.417120e-015  5.686341e-016  2.700775e-015  5.685541e-016
39          1.288117e-011  2.843726e-015  5.686415e-016  2.700801e-015  2.387946e-015
40          1.287895e-011  2.417120e-015  5.686341e-016  2.700775e-015  5.685541e-016
41          1.287360e-011  2.985679e-015  3.790746e-016  1.421419e-015  5.685408e-015
42          1.286341e-011  2.843226e-015  7.580998e-016  2.700563e-015  0.000000e+000
43          1.285435e-011  2.700801e-015  3.790252e-016  2.131920e-015  2.273985e-015
44          1.286341e-011  2.843226e-015  7.580998e-016  2.700563e-015  0.000000e+000
45          1.286904e-011  2.416884e-015  1.326726e-015  2.558504e-015  2.274128e-015
46          1.287168e-011  2.132586e-015  1.895348e-016  2.700669e-015  2.501560e-015
47          1.286904e-011  2.416884e-015  1.326726e-015  2.558504e-015  2.274128e-015
48          1.286341e-011  2.843226e-015  7.580998e-016  2.700563e-015  0.000000e+000
49          1.285435e-011  2.700801e-015  3.790252e-016  2.131920e-015  2.273985e-015
          ];

RELERR3 = [ % NESTED COARSE/FINE-GRAIN OMP PARALLELISM with 4 (outer), 2 (inner) threads for modified Talbot's method
 1          1.285435e-011  2.700801e-015  3.790252e-016  4.263839e-016  4.889069e-015
 2          1.286341e-011  2.843226e-015  1.895250e-016  2.700563e-015  3.524815e-015
 3          1.286904e-011  2.416884e-015  3.790647e-016  2.558504e-015  2.274128e-015
 4          1.287168e-011  2.132586e-015  1.895348e-016  8.528428e-016  2.501560e-015
 5          1.286904e-011  2.416884e-015  3.790647e-016  2.558504e-015  2.274128e-015
 6          1.286341e-011  2.843226e-015  1.895250e-016  2.700563e-015  3.524815e-015
 7          1.285435e-011  2.700801e-015  3.790252e-016  4.263839e-016  4.889069e-015
 8          1.286341e-011  2.843226e-015  1.895250e-016  2.700563e-015  3.524815e-015
 9          1.287360e-011  2.985679e-015  3.790746e-016  3.269263e-015  5.685408e-015
10          1.287895e-011  3.412405e-015  5.686341e-016  2.700775e-015  5.685541e-016
11          1.288117e-011  2.843726e-015  5.686415e-016  2.700801e-015  5.685586e-016
12          1.287895e-011  3.412405e-015  5.686341e-016  2.700775e-015  5.685541e-016
13          1.287360e-011  2.985679e-015  3.790746e-016  2.274270e-015  4.775743e-015
14          1.286341e-011  2.701065e-015  7.580998e-016  1.705619e-015  2.615185e-015
15          1.286890e-011  2.274714e-015  3.790647e-016  1.705669e-015  1.364477e-015
16          1.287895e-011  3.412405e-015  5.686341e-016  1.705752e-015  5.685541e-016
17          1.288416e-011  2.275070e-015  3.791042e-016  0.000000e+000  2.274270e-016
18          1.288694e-011  2.701698e-015  3.791092e-016  1.705819e-015  1.023429e-015
19          1.288416e-011  2.275070e-015  3.791042e-016  0.000000e+000  2.274270e-016
20          1.287895e-011  3.412405e-015  5.686341e-016  1.705752e-015  5.685541e-016
21          1.286890e-011  2.274714e-015  3.790647e-016  1.705669e-015  1.364477e-015
22          1.287154e-011  2.132586e-015  3.790696e-016  0.000000e+000  1.705609e-015
23          1.288131e-011  2.843726e-015  5.686415e-016  1.705769e-015  1.250829e-015
24          1.288694e-011  2.701698e-015  3.791092e-016  1.705819e-015  1.023429e-015
25          1.288816e-011  2.701751e-015  5.686711e-016  2.132295e-015  5.685763e-016
26          1.288694e-011  2.701698e-015  3.791092e-016  1.705819e-015  1.023429e-015
27          1.288131e-011  2.843726e-015  5.686415e-016  1.705769e-015  1.250829e-015
28          1.287154e-011  2.132586e-015  3.790696e-016  0.000000e+000  1.705609e-015
29          1.286890e-011  2.274714e-015  3.790647e-016  1.705669e-015  1.364477e-015
30          1.287895e-011  3.412405e-015  5.686341e-016  1.705752e-015  5.685541e-016
31          1.288416e-011  2.275070e-015  3.791042e-016  0.000000e+000  2.274270e-016
32          1.288694e-011  2.701698e-015  3.791092e-016  1.705819e-015  1.023429e-015
33          1.288416e-011  2.275070e-015  3.791042e-016  0.000000e+000  2.274270e-016
34          1.287895e-011  3.412405e-015  5.686341e-016  1.705752e-015  5.685541e-016
35          1.286890e-011  2.274714e-015  3.790647e-016  1.705669e-015  1.364477e-015
36          1.286341e-011  2.701065e-015  7.580998e-016  1.705619e-015  2.615185e-015
37          1.287360e-011  2.985679e-015  3.790746e-016  2.274270e-015  4.775743e-015
38          1.287895e-011  3.412405e-015  5.686341e-016  1.705752e-015  5.685541e-016
39          1.288131e-011  2.843726e-015  5.686415e-016  1.705769e-015  1.250829e-015
40          1.287895e-011  3.412405e-015  5.686341e-016  1.705752e-015  5.685541e-016
41          1.287360e-011  2.985679e-015  3.790746e-016  2.274270e-015  4.775743e-015
42          1.286341e-011  2.701065e-015  7.580998e-016  1.705619e-015  2.615185e-015
43          1.285435e-011  2.700801e-015  3.790252e-016  1.279152e-015  4.093174e-015
44          1.286341e-011  2.701065e-015  7.580998e-016  1.705619e-015  2.615185e-015
45          1.286890e-011  2.274714e-015  3.790647e-016  1.705669e-015  1.364477e-015
46          1.287154e-011  2.132586e-015  3.790696e-016  0.000000e+000  1.705609e-015
47          1.286890e-011  2.274714e-015  3.790647e-016  1.705669e-015  1.364477e-015
48          1.286341e-011  2.701065e-015  7.580998e-016  1.705619e-015  2.615185e-015
49          1.285435e-011  2.700801e-015  3.790252e-016  1.279152e-015  4.093174e-015
          ];

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

