Alternating group explicit method with exponential-type for the diffusion–convection equation

Feng, Xiufang; Tian, Zhenfu

doi:10.1080/00207160601084463

Cited by 14 publications

(5 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This confirms an earlier work by Feng and Tian [13]. In addition, this observation validates the interesting physics brought to play by the introduction of the memory term in the C-D equation.…”

Section: Numerical Test Examplessupporting

confidence: 78%

See 1 more Smart Citation

A Domain-Boundary Integral Treatment of Transient Scalar Transport with Memory

Onyejekwe¹

2016

View full text Add to dashboard Cite

It is well known that the boundary element method (BEM) is capable of converting a boundaryvalue equation into its discrete analog by a judicious application of the Green's identity and complementary equation. However, for many challenging problems, the fundamental solution is either not available in a cheaply computable form or does not exist at all. Even when the fundamental solution does exist, it appears in a form that is highly non-local which inadvertently leads to a system of equations with a fully populated matrix. In this paper, fundamental solution of an auxiliary form of a governing partial differential equation coupled with the Green identity is used to discretize and localize an integro-partial differential transport equation by conversion into a boundary-domain form amenable to a hybrid boundary integral numerical formulation. It is observed that the numerical technique applied herein is able to accurately represent numerical and closed form solutions available in literature.

show abstract

Section: Numerical Test Examplessupporting

confidence: 78%

“…The numerical solution has been found to develop a steep front or boundary layers at x = 1 (Feng and Tian 2006). Profiles of the numerical solution of equation (21) …”

Section: Numerical Test Examplesmentioning

confidence: 99%

A Domain-Boundary Integral Treatment of Transient Scalar Transport with Memory

Onyejekwe¹

2016

View full text Add to dashboard Cite

show abstract

“…Using the group explicit method, Evans and Abdullah [34] developed the alternating group explicit (AGE) method, which could be solved in an explicit manner and extended to treating other problems. Inspired by the ideas of Evans and Abdullah, authors of [35] used the integral transformation for convection diffusion equation and proposed a scheme which has the truncation error of order Oðk þ h 2 Þ and is unconditionally stable. Zheng [36] proposed a class of alternating group explicit iterative method (AGI) for solving Eq.…”

Section: Introductionmentioning

confidence: 99%

High-order compact solution of the one-dimensional heat and advection–diffusion equations

Mohebbi

Dehghan

2010

Applied Mathematical Modelling

142

View full text Add to dashboard Cite

Compact finite difference scheme Parabolic partial differential equations Stability and high accuracy a b s t r a c tIn this work, we propose a high-order accurate method for solving the one-dimensional heat and advection-diffusion equations. We apply a compact finite difference approximation of fourth-order for discretizing spatial derivatives of these equations and the cubic C 1 -spline collocation method for the resulting linear system of ordinary differential equations. The cubic C 1 -spline collocation method is an A-stable method for time integration of parabolic equations. The proposed method has fourth-order accuracy in both space and time variables, i.e. this method is of order Oðh 4 ; k 4 Þ. Additional to high-order of accuracy, the proposed method is unconditionally stable which will be proved in this paper. Numerical results show that the compact finite difference approximation of fourth-order and the cubic C 1 -spline collocation method give an efficient method for solving the one-dimensional heat and advection-diffusion equations.

show abstract

“…Kara and Zhang [11] introduced an ADI method for an unsteady CDE. Feng and Tian [12] presented an alternating group explicit method for the CDE. Mittal and Jain [13] redefined the cubic B-spline collocation method for solving the CDE.…”

Section: Introductionmentioning

confidence: 99%

Novel Cubic Trigonometric B-Spline Approach Based on the Hermite Formula for Solving the Convection-Diffusion Equation

Yousaf

Abdeljawad

Yaseen

et al. 2020

Mathematical Problems in Engineering

View full text Add to dashboard Cite

This paper introduces a cubic trigonometric B-spline method (CuTBM) based on the Hermite formula for numerically handling the convection-diffusion equation (CDE). The method utilizes a merger of the CuTBM and the Hermite formula for the approximation of a space derivative, while the time derivative is discretized using a finite difference scheme. This combination has greatly enhanced the accuracy of the scheme. A stability analysis of the scheme is also presented to confirm that the errors do not magnify. The main advantage of the scheme is that the approximate solution is obtained as a smooth piecewise continuous function empowering us to approximate a solution at any location in the domain of interest with high accuracy. Numerical tests are performed, and the outcomes are compared with the ones presented previously to show the superiority of the presented scheme.

show abstract

Alternating group explicit method with exponential-type for the diffusion–convection equation

Cited by 14 publications

References 7 publications

A Domain-Boundary Integral Treatment of Transient Scalar Transport with Memory

A Domain-Boundary Integral Treatment of Transient Scalar Transport with Memory

High-order compact solution of the one-dimensional heat and advection–diffusion equations

Novel Cubic Trigonometric B-Spline Approach Based on the Hermite Formula for Solving the Convection-Diffusion Equation

Contact Info

Product

Resources

About