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

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