Mathematical Problems in Engineering / 2021 / Article / Tab 2 / Research Article
Three-Dimensional Fourth-Order Time-Fractional Parabolic Partial Differential Equations and Their Analytical Solution Table 2 Fifth-order approximate numerical solution of equation (
20 ) at different values of the fractional order
α and the absolute error
E = |
u exact –
u α = 1 | for
u (
x ,
y ,
z ,
t ) by FRDTM.
x y z t FRDTM for different values of α u exact Error (E ) α = 0.5α = 0.7α = 0.9α = 10.1 0.3 0.2 0.3 −1.57206 −1.61233 −1.68227 −1.72641 −1.72641 0 0.5 −1.47993 −1.43721 −1.41053 −1.41342 −1.41346 4E − 05 0.8 0.3 −0.97616 −1.00116 −1.04459 −1.072 −1.072 0 0.5 −0.918948 −0.892426 −0.875856 −0.877649 −0.877679 3E − 05 0.4 0.6 0.2 0.3 −1.02973 −1.05611 −1.10192 −1.13083 −1.13083 0 0.5 −0.969381 −0.941403 −0.923924 −0.925816 −0.925847 3.1E − 05 0.8 0.3 −0.43383 −0.444942 −0.464243 −0.476422 −0.476423 1E − 06 0.5 −0.408403 −0.396616 −0.389252 −0.390049 −0.390062 1.3E − 05 0.7 0.9 0.2 0.3 −0.382167 −0.391956 −0.408958 −0.419687 −0.419687 0 0.5 −0.359768 −0.349384 −0.342897 −0.3436 −0.343611 1.1E − 05 0.8 0.3 0.213737 0.219212 0.228721 0.234721 0.234722 1E − 06 0.5 0.20121 0.195403 0.191775 0.192167 0.192174 7E − 06 1 1 0.2 0.3 0.0939895 0.096397 0.100579 0.103217 0.103217 0 0.5 0.0884808 0.0859271 0.0843317 0.0845044 0.0845072 2.8E − 06 0.8 0.3 0.689893 0.707565 0.738258 0.757625 0.757626 1E − 06 0.5 0.649459 0.630714 0.619004 0.620271 0.620292 2.1E − 05