A Modified Laguerre Matrix Approach for Burgers–Fisher Type Nonlinear Equations

Gürbüz, Burcu; Sezer, Mehmet

doi:10.1007/978-3-030-37141-8_6

Cited by 6 publications

(4 citation statements)

References 29 publications

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“…Therefore, the last rows of the augmented matrix ( 38) is reestablished by the row matrix (39) in order to get an approximate solution of Eq. ( 3) under the condition (4).…”

Section: Methods Of Solutionmentioning

confidence: 99%

“…The Laguerre polynomials are important in the applications of quantum theory in the hydrogen atom concept, chemical and mathematical physics [37]. They play an important role at the numerical methods in applied mathematics field such as Laguerre collocation method [38], [39], [40], [41], Laguerre spectral method [42]- [43], Laguerre pseudospectral method [44], and Laguerre wavelets collocation method [45]. Besides, they support the improvement of the numerical solutions by combining with other numerical techniques, i.e.…”

Section: Preliminariesmentioning

confidence: 99%

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A computational approximation for the solution of retarded functional differential equations and their applications to science and engineering

Gürbüz

2022

JIMO

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Delay differential equations are of great importance in science, engineering, medicine and biological models. These type of models include time delay phenomena which is helpful for characterising the real-world applications in machine learning, mechanics, economics, electrodynamics and so on. Besides, special classes of functional differential equations have been investigated in many researches. In this study, a numerical investigation of retarded type of these models together with initial conditions are introduced. The technique is based on a polynomial approach along with collocation points which maintains an approximated solutions to the problem. Besides, an error analysis of the approximate solutions is given. Accuracy of the method is shown by the results. Consequently, illustrative examples are considered and detailed analysis of the problem is acquired. Consequently, the future outlook is discussed in conclusion.

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“…Therefore, the last rows of the augmented matrix ( 38) is reestablished by the row matrix (39) in order to get an approximate solution of Eq. ( 3) under the condition (4).…”

Section: Methods Of Solutionmentioning

confidence: 99%

Section: Preliminariesmentioning

confidence: 99%

A computational approximation for the solution of retarded functional differential equations and their applications to science and engineering

Gürbüz

2022

JIMO

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“…In her study, singularly perturbed secondorder delay parabolic convection-diffusion and reaction-diffusion type problems involving boundary and initial conditions are considered and their approximate solutions are obtained by a matrix method based on Laguerre series. (Here we refer to Ansari et al, 2007, Salama et al, 2017, Gürbüz et al, 2017, Gürbüz et al, 2018, Gürbüz et al, 2019, Gürbüz et al, 2020 The approximate solution of the problem is obtained by truncated Laguerre series. Moreover, a test case is given and the error analysis is considered addressing different norms in order to show the applicability of the method.…”

Section: Published Researchmentioning

confidence: 99%

Editorial – Preface to the Special Issue on Numerical Techniques Meet with OR

Gürbüz

Weber

2021

Foundations of Computing and Decision Sciences

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This special issue of the Foundations of Computing and Decision Sciences, titled ”Numerical Techniques Meet with OR”, is devoted to the numerical techniques and their applications in real-world phenomena. The special issue and its editorial present numerical algorithms as they meet with different research topics such as, e.g., from operational research, supply chain management, geometrical structures and Covid-19 effects on financial applications. Besides, the special issue covers instructional information about numerical techniques which are useful for OR research problems and real-world applications on such issues.

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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. Singh et al [4] constructed a fourth-order B-spline collocation method; in this method, the Crank-Nicolson scheme is used for the discretization, and the Quasi-linearization is used for obtained nonlinear equations.…”

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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A Modified Laguerre Matrix Approach for Burgers–Fisher Type Nonlinear Equations

Cited by 6 publications

References 29 publications

A computational approximation for the solution of retarded functional differential equations and their applications to science and engineering

A computational approximation for the solution of retarded functional differential equations and their applications to science and engineering

Editorial – Preface to the Special Issue on Numerical Techniques Meet with OR

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

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