Linearized Implicit Numerical Method for Burgers’ Equation

Mukundan, Vijitha; Awasthi, Ashish

doi:10.1515/nleng-2016-0031

Cited by 17 publications

(6 citation statements)

References 36 publications

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“…Here, we observe that accuracy improves on increasing M . We take

normalΔ t = 0.01, normalΔ x = 0.0125

, and

ν_{d} = 0.2

in Table 3 and observe that the present method has better accuracy compared to the method of line in Mukundan and Awasthi 57 and higher order time integration method in Verma and Verma 41 . Table 4 represents accuracy of the current scheme at higher time T with

normalΔ x = 0.0125, ν_{d} = 0.01

, and

normalΔ t = 0.01

.…”

Section: Numerical Illustrationsmentioning

confidence: 96%

On a weakly L‐stable time integration formula coupled with nonstandard finite difference scheme with application to nonlinear parabolic partial differential equations

Rawani

Verma

et al. 2021

Math Methods in App Sciences

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In the present paper, we establish an efficient numerical scheme based on weakly L‐stable time integration convergent formula and nonstandard finite difference (NSFD) scheme. We solve Burgers' equation with Dirichlet boundary conditions as well as Neumann boundary conditions. We also solve the Fisher equation. We use Hermite approximation polynomial of order five and backward explicit Taylor's series approximation of order six to derive the numerical integration formula for the initial value problem (IVP) y′false(tfalse)=gfalse(t,yfalse),0.1emyfalse(t0false)=ρ0. We combine this method with the NSFD scheme and convert the problem into the system of algebraic equations. We discuss the convergence, truncation error, and stability of the developed method. To demonstrate the efficiency of the developed method, we compare the numerical results with some existing numerical results and exact solutions.

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“…Here, we observe that accuracy improves on increasing M . We take

normalΔ t = 0.01, normalΔ x = 0.0125

, and

ν_{d} = 0.2

normalΔ x = 0.0125, ν_{d} = 0.01

, and

normalΔ t = 0.01

.…”

Section: Numerical Illustrationsmentioning

confidence: 96%

On a weakly L‐stable time integration formula coupled with nonstandard finite difference scheme with application to nonlinear parabolic partial differential equations

Rawani

Verma

et al. 2021

Math Methods in App Sciences

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“…The Modified Crank-Nicolson method, known for its implicit and stable nature, has proven successful in solving parabolic partial differential equations, making it a promising candidate for modeling complex fluid dynamics within porous structures. The method's ability to handle non-linear terms efficiently further enhances its suitability for applications like the Burgers' equation, which is often utilized to model non-linear behaviors in fluid flow [12,13]. Several studies have applied the Modified Crank-Nicolson method to investigate fluid flow in porous media, demonstrating its accuracy and stability.…”

Section: Literature Reviewmentioning

confidence: 99%

Numerical Modeling of Fluid Flow Through Porous Media: A Modified Crank-Nicolson Approach to Burgers' Equation

Sharma,

Pathak,

Trivedi

2024

JAZ

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This study presents a numerical modeling approach to investigate fluid flow through porous media, focusing on the application of the Modified Crank-Nicolson method to solve the Burgers' equation. The Burgers' equation, known for capturing non-linear features in fluid dynamics, serves as a pertinent model for porous media flow. The Modified Crank-Nicolson method, a variation of the traditional Crank-Nicolson technique, renowned for its stability and accuracy in solving parabolic partial differential equations, is employed to simulate the temporal evolution of fluid flow within the porous medium. Numerical experiments are conducted to explore the dynamic behavior of the system, considering various parameters and boundary conditions. The results showcase the efficacy of the Modified Crank-Nicolson approach in providing insights into the complex phenomena associated with fluid flow through porous media. This research contributes to the broader understanding of numerical methods in porous media dynamics and establishes a foundation for further investigations in related fields.

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“…A fim de se analisar a estabilidade desta aproximação numérica usase o esquema exponencial de von Neumann [14], [19] no qual tem-se um fator de crescimento por meio de um modo de Fourier:…”

Section: Equação De Burgers Com Viscosidadeunclassified

Método numérico adaptativo baseado em wavelets

SILVA¹

2022

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Linearized Implicit Numerical Method for Burgers’ Equation

Cited by 17 publications

References 36 publications

On a weakly L‐stable time integration formula coupled with nonstandard finite difference scheme with application to nonlinear parabolic partial differential equations

On a weakly L‐stable time integration formula coupled with nonstandard finite difference scheme with application to nonlinear parabolic partial differential equations

Numerical Modeling of Fluid Flow Through Porous Media: A Modified Crank-Nicolson Approach to Burgers' Equation

Método numérico adaptativo baseado em wavelets

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