Theory and Modern Applications
Table 1 Comparison of HPETM and RDTM solutions of different fractional-order results at γ of Example 1
From: An efficient approach for solution of fractional-order Helmholtz equations
μ(x,y) | HPETM | HPETM | HPETM | RDTM | RDTM |
|---|---|---|---|---|---|
γ = 1.5 | γ = 1.7 | γ = 2 | γ = 1.7 | γ = 2 | |
(0.1,0.1) | 9.8994158 × 10−4 | 1.8951426 × 10−6 | 4.4682560 × 10−8 | 1.8951426 × 10−6 | 4.4682560 × 10−8 |
(0.2,0.2) | 9.5789042 × 10−3 | 9.7686054 × 10−6 | 9.8994158 × 10−8 | 9.4137771 × 10−6 | 9.7686054 × 10−8 |
(0.3,0.3) | 1.6770296 × 10−3 | 1.9457270 × 10−5 | 9.8994158 × 10−7 | 1.8868189 × 10−5 | 1.9457270 × 10−7 |
(0.4,0.4) | 1.9696739 × 10−2 | 2.8187283 × 10−5 | 2.9025947 × 10−6 | 2.8187283 × 10−5 | 2.9025947 × 10−6 |
(0.5,0.5) | 2.9389443 × 10−2 | 3.7373595 × 10−4 | 3.8474635 × 10−6 | 3.7373595 × 10−4 | 3.8474635 × 10−6 |
(0.6,0.6) | 3.8973948 × 10−2 | 4.6424252 × 10−4 | 4.7800451 × 10−5 | 4.6424252 × 10−4 | 4.7800451 × 10−5 |
(0.7,0.7) | 4.8445597 × 10−2 | 5.5332903 × 10−4 | 5.6998309 × 10−5 | 5.5332903 × 10−4 | 5.6998309 × 10−5 |
(0.8,0.8) | 5.7798601 × 10−2 | 6.4090547 × 10−4 | 6.6061216 × 10−5 | 6.4090547 × 10−4 | 6.6061216 × 10−5 |
(0.9,0.9) | 6.7025983 × 10−2 | 7.2685898 × 10−4 | 7.4980409 × 10−5 | 7.2685898 × 10−4 | 7.4980409 × 10−5 |
(1.0,1.0) | 7.6119511 × 10−2 | 8.1105544 × 10−4 | 8.3745391 × 10−5 | 8.1105544 × 10−4 | 8.3745391 × 10−5 |