scholarly journals The Higher Accuracy Fourth-Order IADE Algorithm

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
N. Abu Mansor ◽  
A. K. Zulkifle ◽  
N. Alias ◽  
M. K. Hasan ◽  
M. J. N. Boyce
Keyword(s):  
Finite Difference ◽  
Heat Equation ◽  
Fourth Order ◽  
Linear Equations ◽  
Dirichlet Boundary Conditions ◽  
The Novel ◽  
One Dimensional ◽  
Systems Of Linear Equations ◽  
The One ◽  
Successive Over Relaxation

This study develops the novel fourth-order iterative alternating decomposition explicit (IADE) method of Mitchell and Fairweather (IADEMF4) algorithm for the solution of the one-dimensional linear heat equation with Dirichlet boundary conditions. The higher-order finite difference scheme is developed by representing the spatial derivative in the heat equation with the fourth-order finite difference Crank-Nicolson approximation. This leads to the formation of pentadiagonal matrices in the systems of linear equations. The algorithm also employs the higher accuracy of the Mitchell and Fairweather variant. Despite the scheme’s higher computational complexity, experimental results show that it is not only capable of enhancing the accuracy of the original corresponding method of second-order (IADEMF2), but its solutions are also in very much agreement with the exact solutions. Besides, it is unconditionally stable and has proven to be convergent. The IADEMF4 is also found to be more accurate, more efficient, and has better rate of convergence than the benchmarked fourth-order classical iterative methods, namely, the Jacobi (JAC4), the Gauss-Seidel (GS4), and the successive over-relaxation (SOR4) methods.

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.

A method for the numerical integration of the one-dimensional heat equation using chebyshev series

1961 ◽  
Vol 57 (4) ◽  
pp. 823-832 ◽  
Author(s):  
David Elliott
Keyword(s):  
Finite Difference ◽  
Heat Equation ◽  
Finite Difference Methods ◽  
Linear Boundary ◽  
Chebyshev Series ◽  
One Dimensional ◽  
Difference Methods ◽  
The One ◽  
Image Position ◽  
General Linear Boundary Conditions

ABSTRACTA numerical solution ofwith general linear boundary conditions alongx= ±1, is described where at any timetthe Chebyshev expansion of θ(x,t) in –1 ≤x≤ 1 is computed directly. Compared with the more usual finite difference methods, this method requires much less computation and there are no stability problems. Two cases are considered in detail.

scholarly journals Numerical Simulation of 1D Unsteady Heat Conduction-Convection in Spherical and Cylindrical Coordinates by Fourth-Order FDM

2018 ◽  
Vol 8 (1) ◽  
pp. 2389-2392
Author(s):  
E. C. Romao ◽  
L. H. P. De Assis
Keyword(s):  
Numerical Simulation ◽  
Heat Conduction ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Fourth Order ◽  
Spherical Coordinates ◽  
Cylindrical Coordinates ◽  
One Dimensional ◽  
Unsteady Heat Conduction ◽  
The One

This paper aims to apply the Fourth Order Finite Difference Method (FDM) to solve the one-dimensional unsteady conduction-convection equation with energy generation (or sink) in cylindrical and spherical coordinates. Two applications were compared through exact solutions to demonstrate the accuracy of the proposed formulation.

scholarly journals On a stochastic Burgers equation with Dirichlet boundary conditions

2003 ◽  
Vol 2003 (43) ◽  
pp. 2735-2746 ◽  
Author(s):  
Ekaterina T. Kolkovska
Keyword(s):  
Weak Solution ◽  
Boundary Conditions ◽  
Dirichlet Boundary ◽  
Burgers Equation ◽  
Martingale Problem ◽  
Weak Limit ◽  
Dirichlet Boundary Conditions ◽  
One Dimensional ◽  
Stochastic Burgers Equation ◽  
The One

We consider the one-dimensional Burgers equation perturbed by a white noise term with Dirichlet boundary conditions and a non-Lipschitz coefficient. We obtain existence of a weak solution proving tightness for a sequence of polygonal approximations for the equation and solving a martingale problem for the weak limit.

scholarly journals One-Dimensional Vacuum Steady Seepage Model of Unsaturated Soil and Finite Difference Solution

2017 ◽  
Vol 2017 ◽  
pp. 1-7 ◽  
Author(s):  
Feng Huang ◽  
Jianguo Lyu ◽  
Guihe Wang ◽  
Hongyan Liu
Keyword(s):  
Finite Difference ◽  
Unsaturated Soil ◽  
Vacuum Pressure ◽  
Vacuum Field ◽  
One Dimensional ◽  
Steady Seepage ◽  
Basic Equations ◽  
The One ◽  
Seepage Law ◽  
Relationship Of

Vacuum tube dewatering method and light well point method have been widely used in engineering dewatering and foundation treatment. However, there is little research on the calculation method of unsaturated seepage under the effect of vacuum pressure which is generated by the vacuum well. In view of this, the one-dimensional (1D) steady seepage law of unsaturated soil in vacuum field has been analyzed based on Darcy’s law, basic equations, and finite difference method. First, the gravity drainage ability is analyzed. The analysis presents that much unsaturated water can not be drained off only by gravity effect because of surface tension. Second, the unsaturated vacuum seepage equations are built up in conditions of flux boundary and waterhead boundary. Finally, two examples are analyzed based on the relationship of matric suction and permeability coefficient after boundary conditions are determined. The results show that vacuum pressure will significantly enhance the drainage ability of unsaturated water by improving the hydraulic gradient of unsaturated water.

Sign in / Sign up

Export Citation Format

Share Document