scholarly journals Fourth-order convergence of a compact scheme for the one-dimensional biharmonic equation

2012 ◽  
Author(s):  
D. Fishelov ◽  
M. Ben-Artzi ◽  
J.-P. Croisille
Keyword(s):  
Fourth Order ◽  
Biharmonic Equation ◽  
Compact Scheme ◽  
Order Convergence ◽  
One Dimensional ◽  
The One

scholarly journals Time-Compact Scheme for the One-Dimensional Dirac Equation

2016 ◽  
Vol 2016 ◽  
pp. 1-8
Author(s):  
Jun-Jie Cao ◽  
Xiang-Gui Li ◽  
Jing-Liang Qiu ◽  
Jing-Jing Zhang
Keyword(s):  
Dirac Equation ◽  
Fourth Order ◽  
Compact Scheme ◽  
Order Accuracy ◽  
Spectral Order ◽  
Unconditionally Stable ◽  
Numerical Examples ◽  
One Dimensional ◽  
The One ◽  
Discrete Charge

Based on the Lie-algebra, a new time-compact scheme is proposed to solve the one-dimensional Dirac equation. This time-compact scheme is proved to satisfy the conservation of discrete charge and is unconditionally stable. The time-compact scheme is of fourth-order accuracy in time and spectral order accuracy in space. Numerical examples are given to test our results.

scholarly journals Fourth-Order Deferred Correction Scheme for Solving Heat Conduction Problem

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
D. Yambangwai ◽  
N. P. Moshkin
Keyword(s):  
Fourth Order ◽  
Heat Conduction Problem ◽  
Correction Method ◽  
Dirichlet Boundary Conditions ◽  
Heat Conducting ◽  
One Dimensional ◽  
Deferred Correction ◽  
The Stability ◽  
The One ◽  
Nicolson Scheme

A deferred correction method is utilized to increase the order of spatial accuracy of the Crank-Nicolson scheme for the numerical solution of the one-dimensional heat equation. The fourth-order methods proposed are the easier development and can be solved by using Thomas algorithms. The stability analysis and numerical experiments have been limited to one-dimensional heat-conducting problems with Dirichlet boundary conditions and initial data.

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