An exponentially fitted numerical technique for singularly perturbed Burgers-Fisher equation on a layer adapted mesh

Sangwan, Vivek; Kaur, Brehmit

doi:10.1080/00207160.2018.1519552

Cited by 7 publications

(4 citation statements)

References 11 publications

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“…As observed from the table, the IELTDM offers more accurate numerical results with far fewer dof. Even the problem behaves highly stiff with D≪1, the IELDTM produces highly accurate results instead of the FEM presented in (Sangwan and Kaur, 2019). Advection-dominated cases of Burgers–Fisher equation with D≪V are highly challenging due to the sharp behaviours of the solutions.…”

Section: Numerical Experimentsmentioning

confidence: 99%

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An implicit-explicit local method for parabolic partial differential equations

Tunc

Sarı

2021

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PurposeThe purpose of this article is to derive an implicit-explicit local differential transform method (IELDTM) in dealing with the spatial approximation of the stiff advection-diffusion-reaction (ADR) equations.Design/methodology/approachA direction-free numerical approach based on local Taylor series representations is designed for the ADR equations. The differential equations are directly used for determining the local Taylor coefficients and the required degrees of freedom is minimized. The complete system of algebraic equations is constructed with explicit/implicit continuity relations with respect to direction parameter. Time integration of the ADR equations is continuously utilized with the Chebyshev spectral collocation method.FindingsThe IELDTM is proven to be a robust, high order, stability preserved and versatile numerical technique for spatial discretization of the stiff partial differential equations (PDEs). It is here theoretically and numerically shown that the order refinement (p-refinement) procedure of the IELDTM does not affect the degrees of freedom, and thus the IELDTM is an optimum numerical method. A priori error analysis of the proposed algorithm is done, and the order conditions are determined with respect to the direction parameter.Originality/valueThe IELDTM overcomes the known disadvantages of the differential transform-based methods by providing reliable convergence properties. The IELDTM is not only improving the existing Taylor series-based formulations but also provides several advantages over the finite element method (FEM) and finite difference method (FDM). The IELDTM offers better accuracy, even when using far less degrees of freedom, than the FEM and FDM. It is proven that the IELDTM produces solutions for the advection-dominated cases with the optimum degrees of freedom without producing an undesirable oscillation.

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Section: Numerical Experimentsmentioning

confidence: 99%

“…The present IELDTM and the FEM solutions (Sangwan and Kaur, 2019) have been compared in the presence of weak advection and reaction effects with various values of diffusion coefficient D in Table 3. As observed from the table, the IELTDM offers more accurate numerical results with far fewer dof.…”

Section: Numerical Experimentsmentioning

confidence: 99%

An implicit-explicit local method for parabolic partial differential equations

Tunc

Sarı

2021

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“…The development of inbound tourism is conducive to the industrial transformation of the region. It promotes the industrial transfer of the three significant east, middle and west areas to achieve coordinated regional development [2].…”

Section: Introductionmentioning

confidence: 99%

“…We make ∥υ∥ 2 Z,n = max tn ≤ t ≤ t n+1 ∥υ(t)∥ Z , where Z = X (or Y) I n ⊆ J. For s, m = 0, 1, • • • and υ ∈ H m (Ω), we define the discrete norm ∥h s n υ∥ m,h = (∑ r∈T n h h 2s τ ∥υ∥ 2 m,τ ) 1 2 . Let u(0, x) = u 0 (x) have the following equation:…”

Section: Introductionmentioning

confidence: 99%

Research on tourism income index based on ordinary differential mathematical equation

Xiong¹

2022

Applied Mathematics and Nonlinear Sciences

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Economic benefits continue to increase with the rapid development of the tourism industry. The level of tourism development is an indicator to measure the maturity of a country’s tourism industry. The article takes China’s coastal provinces as the research object and uses finite element ordinary differential mathematical equations to explore the income indicators of the tourism industry in coastal cities. In the dynamic process, the article portrays the development trend of tourism in different regions. It analyses the income levels and indicators of tourism development in coastal cities under different time and space conditions. The research results show that we can divide the time zone to count the base period value and average growth rate of domestic tourism in each province to classify the regional response type of domestic tourism development.

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

Gürbüz

Sezer

2020

Nonlinear Systems and Complexity

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An exponentially fitted numerical technique for singularly perturbed Burgers-Fisher equation on a layer adapted mesh

Cited by 7 publications

References 11 publications

An implicit-explicit local method for parabolic partial differential equations

An implicit-explicit local method for parabolic partial differential equations

Research on tourism income index based on ordinary differential mathematical equation

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

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