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Table 5 Table of absolute errors in the maximum norm and spatial 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

  τ = 5 × 10−4 τ = 2.5 × 10−4 τ = 1.25 × 10−4
h \(\epsilon _{t, h}\) \(\rho _{h}\) \(\epsilon _{t, h}\) \(\rho _{h}\) \(\epsilon _{t, h}\) \(\rho _{h}\)
T = 1
2/20 2.72891640 × 10−3 7.38903899 × 10−4 1.92801667 × 10−4
2/21 6.08617515 × 10−4 2.16472044 1.53496126 × 10−4 2.26718449 4.23532511 × 10−5 2.18657290
2/22 1.23264181 × 10−4 2.30378222 3.31398131 × 10−5 2.21156488 9.55526103 × 10−6 2.14810553
2/23 2.40756903 × 10−5 2.35610456 6.97944970 × 10−6 2.24738027 2.24943767 × 10−6 2.08673089
2/24 5.35953443 × 10−6 2.16739758 1.57552357 × 10−6 2.14728195 5.00208668 × 10−7 2.16896243
T = 10
2/20 2.80627843 × 10−3 7.48551627 × 10−4 2.18637328 × 10−4
2/21 5.82837716 × 10−4 2.26749201 1.66642570 × 10−4 2.16734482 5.11309655 × 10−5 2.09627056
2/22 1.29375821 × 10−4 2.17152622 3.94539680 × 10−5 2.07851469 1.13824890 × 10−5 2.16738120
2/23 2.71945685 × 10−5 2.25017758 9.26898876 × 10−6 2.08968655 2.60012534 × 10−6 2.13016299
2/24 6.35975778 × 10−6 2.09627481 2.13604753 × 10−6 2.11746820 6.21903759 × 10−7 2.06381793
T = 50
2/20 2.87820224 × 10−3 7.53867720 × 10−4 2.24422947 × 10−4
2/21 6.50328970 × 10−4 2.14592637 1.66761373 × 10−4 2.17652624 5.03484551 × 10−5 2.15620078
2/22 1.53265284 × 10−4 2.08513874 3.84354956 × 10−5 2.11727398 1.18548423 × 10−5 2.08647103
2/23 3.65707445 × 10−5 2.06726905 9.18431827 × 10−6 2.06519473 2.82647735 × 10−6 2.06839944
2/24 8.84445865 × 10−6 2.04784425 2.22227666 × 10−6 2.04713420 6.81731460 × 10−7 2.05172967