Theory and Modern Applications

# Table 3 Values of the approximate solution of problem (57) at different values of x and $$T = 3$$, using $$\varOmega = (0, \pi )$$, $$\alpha = 1.8$$, and $$K = 0.1$$. Computationally, we used different combinations of values of h and τ. The results were obtained using the EFDA, IFDA, and FMoL reported in [36], as well as the DM method introduced in the present manuscript

Method
x EFDA IFDA FMoL DM method
h = π/200, τ = 0.016
0.3142 1.57368789 1.57372511 1.57392168 1.57372919
0.6283 2.16380277 2.16386523 2.16399150 2.16385886
0.9425 2.33655001 2.33663342 2.33667019 2.33661347
1.2566 2.38754579 2.38764530 2.38762011 2.38761337
1.5708 2.39918437 2.39929592 2.39922930 2.39925392
1.8850 2.38753659 2.38766383 2.38756809 2.38761337
2.1991 2.33650970 2.33667395 2.33654916 2.33661347
2.5133 2.16369084 2.16393561 2.16376674 2.16385886
2.8274 1.57350732 1.57381573 1.57361994 1.57372919
h = π/400, τ = 0.008
0.3142 1.57438633 1.57437820 1.57435879 1.57435676
0.6283 2.16341461 2.16340869 2.16339364 2.16339412
0.9425 2.33597962 2.33597699 2.33597013 2.33597013
1.2566 2.38702266 2.38702177 2.38701950 2.38701864
1.5708 2.39869212 2.39869098 2.39869138 2.39868980
1.8850 2.38702107 2.38701906 2.38702156 2.38701864
2.1991 2.33597346 2.33597038 2.33597368 2.33597013
2.5133 2.16339880 2.16339599 2.16339738 2.16339412
2.8274 1.57436187 1.57436096 1.57436143 1.57435676
h = π/800, τ = 0.004
0.3142 1.57400608 1.57400734 1.57400844 1.57400710
0.6283 2.16262828 2.16262984 2.16263132 2.16263025
0.9425 2.33531356 2.33531372 2.33531405 2.33531388
1.2566 2.38648630 2.38648729 2.38648785 2.38648734
1.5708 2.39820239 2.39820243 2.39820257 2.39820244
1.8850 2.38648651 2.38648731 2.38648785 2.38648734
2.1991 2.33531397 2.33531392 2.33531389 2.33531387
2.5133 2.16263007 2.16263026 2.16263073 2.16263025
2.8274 1.57400875 1.57400804 1.57400742 1.57400710