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Volume 11, Issue 1
An accelerated numerical computation for ....

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Research in Mathematics Volume 11, 2024 - Issue 1

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Pure Mathematics

An accelerated numerical computation for singularly perturbed Robin-type parabolic problems with small parameters

Fasika Wondimu Gelua Department of Mathematics, Dilla University, Dilla, EthiopiaCorrespondence[email protected]

https://orcid.org/0000-0002-4693-9051 View further author information

Gemechis File Duressab Department of Mathematics, Jimma University, Jimma, Ethiopia

https://orcid.org/0000-0003-1889-4690 View further author information

Hari M. Srivastavac Department of Mathematics and Statistics, Department of Mathematics and Statistics, University of VictoriaVictoriaCanada

(Reviewing editor:)

Article: 2354536 | Received 06 Nov 2023, Accepted 08 May 2024, Published online: 22 May 2024

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https://doi.org/10.1080/27684830.2024.2354536
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Table 1. Values of $E_{ε, μ, e x t}^{M, Δ t}, E_{e x t}^{M, Δ t}, R_{e x t}^{M, Δ t}$ , $E_{ε, μ}^{M, Δ t}$ , $E^{M, Δt}, R^{M, Δt}$ for $μ = 10^{- 10}$ fcple (5.1)

Display Table

Table 2. Values of $E_{ε, μ, e x t}^{M, Δ t}, E_{e x t}^{M, Δ t}, R_{e x t}^{M, Δ t}$ , $E_{ε, μ}^{M, Δ t}$ , $E^{M, Δt}, R^{M, Δt}$ for $μ = 10^{- 10}$ for example (5.2)

Display Table

Figure 1. Mesh plot of the numerical solution for example (5.1) at $M = 32 = \frac{1}{Δt}$ .

Figure 1. Mesh plot of the numerical solution for example (5.1) at M=32=1Δt.

Figure 2. Log-log plot of the maximum errors at $μ = 10^{- 10}$ for example (5.1).

Figure 3. Mesh plot of the numerical solution for example (5.2) at $N = 64 = \frac{1}{Δt}$ .

Figure 3. Mesh plot of the numerical solution for example (5.2) at N=64=1Δt.

Figure 4. Log-log plot of the maximum errors at $μ = 10^{- 10}$ for example (5.2).

Table 3. Values of $E_{ε, μ, e x t}^{M, Δ t}, E_{e x t}^{M, Δ t}, R_{e x t}^{M, Δ t}$ , $E_{ε, μ}^{M, Δ t}$ , $E^{M, Δt}, R^{M, Δt}$ for $ε = 10^{- 2}$ for example (5.1)

Display Table

Table 4. Values of $E_{ε, μ, e x t}^{M, Δ t}, E_{e x t}^{M, Δ t}, R_{e x t}^{M, Δ t}$ , $E_{ε, μ}^{M, Δ t}$ , $E^{M, Δt}, R^{M, Δt}$ for $ε = 10^{- 2}$ for example (5.2)

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An accelerated numerical computation for singularly perturbed Robin-type parabolic problems with small parameters

Figures & data

Table 1. Values of Eε,μ,extM,Δt,EextM,Δt,RextM,Δt, Eε,μM,Δt, EM,Δt,RM,Δt for μ=10−10 fcple (5.1)

Table 2. Values of Eε,μ,extM,Δt,EextM,Δt,RextM,Δt, Eε,μM,Δt, EM,Δt,RM,Δt for μ=10−10 for example (5.2)

Table 3. Values of Eε,μ,extM,Δt,EextM,Δt,RextM,Δt, Eε,μM,Δt, EM,Δt,RM,Δt for ε=10−2 for example (5.1)

Table 4. Values of Eε,μ,extM,Δt,EextM,Δt,RextM,Δt, Eε,μM,Δt, EM,Δt,RM,Δt for ε=10−2 for example (5.2)

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Table 1. Values of $E_{ε, μ, e x t}^{M, Δ t}, E_{e x t}^{M, Δ t}, R_{e x t}^{M, Δ t}$ , $E_{ε, μ}^{M, Δ t}$ , $E^{M, Δt}, R^{M, Δt}$ for $μ = 10^{- 10}$ fcple (5.1)

Table 2. Values of $E_{ε, μ, e x t}^{M, Δ t}, E_{e x t}^{M, Δ t}, R_{e x t}^{M, Δ t}$ , $E_{ε, μ}^{M, Δ t}$ , $E^{M, Δt}, R^{M, Δt}$ for $μ = 10^{- 10}$ for example (5.2)

Table 3. Values of $E_{ε, μ, e x t}^{M, Δ t}, E_{e x t}^{M, Δ t}, R_{e x t}^{M, Δ t}$ , $E_{ε, μ}^{M, Δ t}$ , $E^{M, Δt}, R^{M, Δt}$ for $ε = 10^{- 2}$ for example (5.1)

Table 4. Values of $E_{ε, μ, e x t}^{M, Δ t}, E_{e x t}^{M, Δ t}, R_{e x t}^{M, Δ t}$ , $E_{ε, μ}^{M, Δ t}$ , $E^{M, Δt}, R^{M, Δt}$ for $ε = 10^{- 2}$ for example (5.2)