Theory and Modern Applications
Table 4 Table of absolute errors in the maximum norm and temporal rates of convergence for various values of the parameters τ and h. We used \(f (u) = u (1 - u)\), and the exact solution (58) of model (46). We employed also \(\varOmega = (- 200, 200)\) and various values of T
From: Discrete monotone method for space-fractional nonlinear reaction–diffusion equations
h = 1 | h = 0.5 | h = 0.25 | ||||
|---|---|---|---|---|---|---|
τ | \(\epsilon _{\tau, h}\) | \(\rho _{\tau }\) | \(\epsilon _{\tau, h}\) | \(\rho _{\tau }\) | \(\epsilon _{\tau, h}\) | \(\rho _{\tau }\) |
T = 1 | ||||||
0.2/20 | 2.67829504 × 10−2 | − | 1.02746832 × 10−2 | − | 6.86107201 × 10−3 | − |
0.2/21 | 1.39736652 × 10−2 | 0.93860442 | 5.19210974 × 10−3 | 0.98470113 | 3.27302120 × 10−3 | 1.06781106 |
0.2/22 | 6.96832376 × 10−3 | 1.00382692 | 2.42698608 × 10−3 | 1.09715504 | 1.33351771 × 10−3 | 1.29538596 |
0.2/23 | 2.87272809 × 10−3 | 1.27839021 | 1.00672149 × 10−3 | 1.26950121 | 5.21640040 × 10−4 | 1.35411047 |
0.2/24 | 1.27134635 × 10−3 | 1.17606433 | 4.28389417 × 10−4 | 1.23266988 | 2.19716822 × 10−4 | 1.24740928 |
T = 10 | ||||||
0.2/20 | 3.61963008 × 10−2 | − | 1.88368494 × 10−2 | − | 8.75622547 × 10−3 | − |
0.2/21 | 1.94607648 × 10−2 | 0.89527385 | 9.56993064 × 10−3 | 0.97697731 | 4.18864496 × 10−3 | 1.06382550 |
0.2/22 | 8.08362730 × 10−3 | 1.26749370 | 4.53126541 × 10−3 | 1.07859447 | 1.88939130 × 10−3 | 1.14856208 |
0.2/23 | 3.64953553 × 10−3 | 1.14728994 | 2.03288428 × 10−3 | 1.15638590 | 8.88224791 × 10−4 | 1.08892478 |
0.2/24 | 1.74324598 × 10−3 | 1.06593671 | 9.01840414 × 10−4 | 1.17258403 | 4.32223831 × 10−4 | 1.03914622 |
T = 50 | ||||||
0.2/20 | 3.96849776 × 10−2 | − | 1.67291610 × 10−2 | − | 9.28669337 × 10−3 | − |
0.2/21 | 2.02824578 × 10−2 | 0.96836050 | 8.20627788 × 10−3 | 1.02756518 | 4.77745217 × 10−3 | 0.95892357 |
0.2/22 | 9.28799326 × 10−3 | 1.12679366 | 3.90749860 × 10−3 | 1.07048265 | 2.17094911 × 10−3 | 1.13791552 |
0.2/23 | 4.43068565 × 10−3 | 1.06783695 | 1.77641225 × 10−3 | 1.13727893 | 1.02809201 × 10−3 | 1.07835652 |
0.2/24 | 2.08820809 × 10−3 | 1.08526449 | 7.96579516 × 10−4 | 1.15707614 | 5.00554256 × 10−4 | 1.03837103 |