Extended one-step time-integration schemes for convection-diffusion equations

Chawla, M. M.; Al-Zanaidi, M. A.; Al-Aslab, M.G.

doi:10.1016/s0898-1221(99)00334-x

Cited by 23 publications

(12 citation statements)

References 10 publications

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“…The results are computed for different time levels and listed in Table 13. Also we comp our results e that the errors in our method more or less is similar to [1] but the errors in our method are much less than the errors in [9].…”

Section: Th L Solution O Issupporting

confidence: 58%

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Exponential B-Spline Solution of Convection-Diffusion Equations

Mohammadi¹

2013

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We present an exponential B-spline collocation method for solving convection-diffusion equation with Dirichlet's type boundary conditions. The method is based on the Crank-Nicolson formulation for time integration and exponential B-spline functions for space integration. Using the Von Neumann method, the proposed method is shown to be unconditionally stable. Numerical experiments have been conducted to demonstrate the accuracy of the current algorithm with relatively minimal computational effort. The results showed that use of the present approach in the simulation is very applicable for the solution of convection-diffusion equation. The current results are also seen to be more accurate than some results given in the literature. The proposed algorithm is seen to be very good alternatives to existing approaches for such physical applications.

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Section: Th L Solution O Issupporting

confidence: 58%

“…Example 5.6 Consider the following equation [1,23] are results with the results in [1,9]. The indicat The produced results were seen t …”

Section: Th L Solution O Ismentioning

confidence: 99%

Exponential B-Spline Solution of Convection-Diffusion Equations

Mohammadi¹

2013

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“…In [19], they have used a one-parameter family of unconditionally stable third order time-integration scheme with temporal and spatial step sizes being k = 0.25 and h = 0.05, respectively and compared their results with Crank-Nicolson which is highly oscillatory. In this work, we consider four combinations of values of α and h; namely α = 0.01, h = 0.1; α = 0.1, h = 0.05; α = 1, h = 0.05 and α = 1, h = 0.1 and display the numerical results at time, T = 1.…”

Section: Problemmentioning

confidence: 99%

A computational study of three numerical methods for some advection-diffusion problems

Appadu

Djoko

Gidey

2016

Applied Mathematics and Computation

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Three numerical methods have been used to solve two problems described by advection-diffusion equations with specified initial and boundary conditions. The methods used are the third order upwind scheme [4], fourth order upwind scheme [4] and Non-Standard Finite Difference scheme (NSFD) [9]. We considered two test problems. The first test problem has steep boundary layers near x = 1 and this is challenging problem as many schemes are plagued by non-physical oscillation near steep boundaries [15]. Many methods suffer from computational noise when modelling the second test problem especially when the coefficient of diffusivity is very small for instance 0.01. We compute some errors, namely L 2 and L ∞ errors, dissipation and dispersion errors, total variation and the total mean square error for both problems and compare the computational time when the codes are run on a matlab platform. We then use the optimization technique devised by Appadu [1] to find the optimal value of the time step at a given value of the spatial step which minimizes the dispersion error and this is validated by some numerical experiments.

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“…By the analysis of auxiliary difference equations and the maximum principle, authors of [31] showed that this method has second-order global accuracy in space. Chawla et al [32,33] described the one-parameter family of unconditionally stable third and fourth-order time-integration schemes for the convection-diffusion equation based on the extended trapezoidal formulas. These methods have second-order accuracy in spatial component and are unconditionally stable.…”

Section: Introductionmentioning

confidence: 99%

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

Mohebbi

Dehghan

2010

Applied Mathematical Modelling

143

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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.

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Extended one-step time-integration schemes for convection-diffusion equations

Cited by 23 publications

References 10 publications

Exponential B-Spline Solution of Convection-Diffusion Equations

Exponential B-Spline Solution of Convection-Diffusion Equations

A computational study of three numerical methods for some advection-diffusion problems

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

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