High-order solution of Generalized Burgers–Fisher Equation using compact finite difference and DIRK methods

Pirdawood, Mardan A.; Sabawi, Younis A.

doi:10.1088/1742-6596/1999/1/012088

Cited by 7 publications

(3 citation statements)

References 13 publications

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“…Whenever first-order IMEX-RK techniques have generally been applied to deals with the stiff terms of the chemistry implicitly in combustion simulations and hypersonic flow, two IMEX-RK techniques are fourth-order accurate. As a result, there have been several studies that have attracted much interest, and many numerical schemes, like the Euler method, Runge Kutta method, multistep schemes [17-20], Finite difference method [21, [34][35][36][37][38][39][40], and Finite element methods [22][23][24][25], have been proposed over time.…”

Section: The Proposed Methodsmentioning

confidence: 99%

Mathematical Modeling and Analysis for COVID-19 Model by Using Implicit-Explicit Rung-Kutta Methods

et al. 2022

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One of the most common health care problems globally is COVID-19, and also there are an international effort to monitor it have been proposed and discussed. Despite the fact that many studies have been performed based on clinical evidence and confirmed infected cases. However, there is room for additional research since a range of complex criteria are included for later research forecast. As a consequence, mathematical modelling mixed with the numerical simulations is an effective method for estimating main propagation parameters and forecasting disease model dynamics. We study and present some models for the COVID-19 in this paper, which can answer significant questions concerning global health care and implement important notes. The IMEX Runge–Kutta and classical Runge–Kutta methods are two well-known computational schemes to find the solution for such system of differential equations. The results, which are based on these numerical procedures suggested and provide estimated solutions, provide critical answers to this global problem. The amount of recovered, infected, susceptible, and quarantined people in the expectation can be estimated using numerical data. The findings could also aid international efforts to increase prevention and strengthen intervention programs. The findings could also support international efforts to increase prevention and strengthen intervention programs. It is clearly that the proposed methods more accurate and works in a very large interval in time with a few step sizes. That is consequently beginning to a decrease in the computational price of the method. Numerical experiments show that there is a good argument and accurate solutions for solving this type of problem.

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Section: The Proposed Methodsmentioning

confidence: 99%

Mathematical Modeling and Analysis for COVID-19 Model by Using Implicit-Explicit Rung-Kutta Methods

et al. 2022

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“…In addition, we propose a method to avoid the difficulties that appear when the models of ERK cell signalling pathway transfer to stiff nonlinear equations with an implicit method. This method is called Implicit -Explicit (IMEX) schemes for more details [12][13][14][15]. Consider the numerical method of the following system of stiff ordinary differential equation:…”

Section: Introductionmentioning

confidence: 99%

Model Reduction and Analysis for ERK Cell Signalling Pathway Using Implicit-Explicit Rung-Kutta Methods

Rasool

Pirdawood

Sabawi

et al. 2022

PJBAS

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Many complex cell signalling pathways and chemical reaction networks include many variables and parameters; this is sometimes a big issue for identifying critical model elements and describing the model dynamics. Therefore, model reduction approaches can be employed as a mathematical tool to reduce the number of elements. In this study, we use a new technique for model reduction: the Lumping of parameters for the simple linear chemical reaction network and the complex cell signalling pathway that is extracellular-signal-regulated kinase (ERK) pathways. Moreover, we propose a high-order and accurate method for solving stiff nonlinear ordinary differential equations. The curtail idea of this scheme is based on splitting the problem into stiff and non-stiff terms. More specifically, stiff discretization uses the implicit method, and nonlinear discretization uses the explicit method. This is consequently leading to a reduction in the computational cost of the scheme.The main aim of this study is to reduce the complex cell signalling pathway models by proposing an accurate numerical approximation Runge-Kutta method. This improves one's understanding of such behaviour of these systems and gives an accurate approximate solution. Based on the suggested technique, the simple model's parameters are minimized from 6 to 3, and the complex models from 11 to 8. Resultsshow that there is a good agreement between the original models and the simplified models.

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“…Pirdawood and Sabawi [2] proposed an accurate scheme using the compact finite difference method and the Runge Kutta method. Gürbüz and Sezer [3] applied a modified Laguerre matrix-collocation method.…”

Section: Introductionmentioning

confidence: 99%

A numerical Approximation for the One-dimensional Burger–Fisher Equation

Hajinezhad

2022

ARJOM

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In this paper, an implicit finite difference method based on the Crank–Nicolson method is proposed for the numerical solution of the one-dimensional Burger–Fisher equation. The Crank–Nicolson scheme provides a system of nonlinear difference equations, which is solved by an integration of the Jacobian-Free-Newton-Krylov (JFNK) and GMRES methods. Various numerical examples are given to demonstrate the efficiency of the proposed scheme. Comparison of the computed solutions with the analytical ones demonstrates the accuracy of this proposed method.

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High-order solution of Generalized Burgers–Fisher Equation using compact finite difference and DIRK methods

Cited by 7 publications

References 13 publications

Mathematical Modeling and Analysis for COVID-19 Model by Using Implicit-Explicit Rung-Kutta Methods

Mathematical Modeling and Analysis for COVID-19 Model by Using Implicit-Explicit Rung-Kutta Methods

Model Reduction and Analysis for ERK Cell Signalling Pathway Using Implicit-Explicit Rung-Kutta Methods

A numerical Approximation for the One-dimensional Burger–Fisher Equation

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