Generalized trapezoidal formulas for parabolic equations

Al-Zanaidi, M. A.; Evans, David

doi:10.1080/00207169908804765

Cited by 30 publications

(15 citation statements)

References 5 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Recently, Chawla et al [3,4,5,6] have described time integration schemes for parabolic differential equations and for the convection-diffusion equation, in one and two space dimensions, based on the generalized trapezoidal formulas of Chawla et al [2].…”

Section: Introductionmentioning

confidence: 99%

Generalized Trapezoidal Formulas for the Symmetric Heat Equation in Polar Coordinates

Al-Zanaidi

Evans

2002

International Journal of Computer Mathematics

Self Cite

View full text Add to dashboard Cite

This paper has two objectives. We first describe one-step time integration schemes for the symmetric heat equation in polar coordinates: u t ¼ nðu rr þ ða=rÞu r Þ based on the generalized trapezoidal formulas (GTF(a)) of Chawla et al. [2]. This includes the case of cylindrical symmetry for a ¼ 1 and of spherical symmetry for a ¼ 2. The obtained GTF(a) time integration schemes are second order in time and unconditionally stable. We then introduce generalized finite Hankel transforms to obtain an analytical solution of the heat equation for all a 1, with Dirichlet and Neumann type boundary conditions. Numerical experiments are provided to compare the accuracy and stability of the obtained GTF(a) time integration schemes with the schemes based on the backward Euler, the classical arithmetic-mean trapezoidal formula and a third order time integration scheme.

show abstract

Section: Introductionmentioning

confidence: 99%

Generalized Trapezoidal Formulas for the Symmetric Heat Equation in Polar Coordinates

Al-Zanaidi

Evans

2002

International Journal of Computer Mathematics

Self Cite

View full text Add to dashboard Cite

show abstract

“…Recently, Chawla et al [3,4] have described time integration schemes for parabolic differential equations and for the convection-diffusion equation, in one space dimension, based on the generalized trapezoidal formulas (GTF(a)) given in Chawla et al [2].…”

Section: Introductionmentioning

confidence: 99%

Lod generalized trapezoidal formula schemes for parabolic differential equations in two space dimensions

Al-Zanaidi

Evans

2001

International Journal of Computer Mathematics

View full text Add to dashboard Cite

We describe locally one-dimensional (LOD) time integration schemes for parabolic differential equations in two space dimensions, based on the generalized trapezoidal formulas (GTF(a)). We describe the schemes for the diffusion equation with Dirichlet and Neumann boundary conditions, for nonlinear reaction-diffusion equations, and for the convection-diffusion equation in two space dimensions. The obtained schemes are second order in time and unconditionally stable for all a E [0, 11. Numerical experiments are given to illustrate the obtained schemes and to compare their performance with the better known LOD CrankNicolson scheme. While the LOD Crank-Nicolson scheme can give unwanted oscillations in the computed solution, our present LOD-GTF(a) schemes provide both stable and accurate approximations for the true solution.

show abstract

“…In this paper, based on quartic splines and generalized trapezoidal formula [5], a class of unconditionally stable twolevel difference scheme including a parameter θ is proposed to solve the problem (1). The accuracy of the scheme is O(k 2 +h 4 ).…”

Section: Introductionmentioning

confidence: 99%

A New Two Level Difference Scheme for Solving One-Dimensional Second-Order Hyperbolic Equations

Tang-wei

Liu

et al. 2010

2010 Third International Joint Conference on Computational Science and Optimization

View full text Add to dashboard Cite

In this paper, a new numerical method is developed for solving one-dimensional second-order hyperbolic equations.By using a new unconditionally stable two level difference scheme based on the quartic spline interpolation method in space direction and generalized trapezoidal formula in time direction, the hyperbolic equations are solved. Stability analysis of the scheme is carried out. The accuracy of the scheme is second-order in time direction and fourth-order in space direction. It has been shown that by suitably choosing parameter, a high accuracy scheme of third-order accurate in time direction can be derived from the method. Numerical results comparison demonstrate the superiority of the new scheme.

show abstract

Generalized trapezoidal formulas for parabolic equations

Cited by 30 publications

References 5 publications

Generalized Trapezoidal Formulas for the Symmetric Heat Equation in Polar Coordinates

Generalized Trapezoidal Formulas for the Symmetric Heat Equation in Polar Coordinates

Lod generalized trapezoidal formula schemes for parabolic differential equations in two space dimensions

A New Two Level Difference Scheme for Solving One-Dimensional Second-Order Hyperbolic Equations

Contact Info

Product

Resources

About