Numerical comparison of methods for solving parabolic equations

Kamel Al-Khaled, Dogan Kaya, Muhammad Aslam Noor

Research output: Contribution to journalArticle

12 Citations (Scopus)

Abstract

In this paper, we apply a new decomposition scheme to solve the linear heat equation. The approach is based on the choice of a suitable differential operator which may be ordinary or partial, linear or nonlinear, deterministic or stochastic. It does not require discretization and consequently of massive computation. In this scheme the solution is performed in the form of a convergent power series with easily computable components. This paper is particularly concerned with the Adomian decomposition method and the results obtained are compared to those obtained by a conventional finite-difference method and the Sinc method. The numerical results demonstrate that the new method is relatively accurate and easily implemented.

Original languageEnglish
Pages (from-to)735-743
Number of pages9
JournalApplied Mathematics and Computation
Volume157
Issue number3
DOIs
Publication statusPublished - Oct 15 2004

Fingerprint

Numerical Comparisons
Parabolic Equation
Sinc Method
Decomposition
Adomian Decomposition Method
Power series
Finite difference method
Heat Equation
Difference Method
Differential operator
Linear equation
Finite Difference
Discretization
Partial
Decompose
Numerical Results
Demonstrate
Form
Hot Temperature

Keywords

  • A parabolic partial differential equation
  • Finite-difference method
  • Sinc functions
  • The Adomian decomposition method

ASJC Scopus subject areas

  • Applied Mathematics
  • Computational Mathematics
  • Numerical Analysis

Cite this

Numerical comparison of methods for solving parabolic equations. / Al-Khaled, Kamel; Kaya, Dogan; Noor, Muhammad Aslam.

In: Applied Mathematics and Computation, Vol. 157, No. 3, 15.10.2004, p. 735-743.

Research output: Contribution to journalArticle

Al-Khaled, Kamel ; Kaya, Dogan ; Noor, Muhammad Aslam. / Numerical comparison of methods for solving parabolic equations. In: Applied Mathematics and Computation. 2004 ; Vol. 157, No. 3. pp. 735-743.
@article{0d6dbeb6a86947fa97ff317d7a596ee5,
title = "Numerical comparison of methods for solving parabolic equations",
abstract = "In this paper, we apply a new decomposition scheme to solve the linear heat equation. The approach is based on the choice of a suitable differential operator which may be ordinary or partial, linear or nonlinear, deterministic or stochastic. It does not require discretization and consequently of massive computation. In this scheme the solution is performed in the form of a convergent power series with easily computable components. This paper is particularly concerned with the Adomian decomposition method and the results obtained are compared to those obtained by a conventional finite-difference method and the Sinc method. The numerical results demonstrate that the new method is relatively accurate and easily implemented.",
keywords = "A parabolic partial differential equation, Finite-difference method, Sinc functions, The Adomian decomposition method",
author = "Kamel Al-Khaled and Dogan Kaya and Noor, {Muhammad Aslam}",
year = "2004",
month = "10",
day = "15",
doi = "10.1016/j.amc.2003.08.079",
language = "English",
volume = "157",
pages = "735--743",
journal = "Applied Mathematics and Computation",
issn = "0096-3003",
publisher = "Elsevier Inc.",
number = "3",

}

TY - JOUR

T1 - Numerical comparison of methods for solving parabolic equations

AU - Al-Khaled, Kamel

AU - Kaya, Dogan

AU - Noor, Muhammad Aslam

PY - 2004/10/15

Y1 - 2004/10/15

N2 - In this paper, we apply a new decomposition scheme to solve the linear heat equation. The approach is based on the choice of a suitable differential operator which may be ordinary or partial, linear or nonlinear, deterministic or stochastic. It does not require discretization and consequently of massive computation. In this scheme the solution is performed in the form of a convergent power series with easily computable components. This paper is particularly concerned with the Adomian decomposition method and the results obtained are compared to those obtained by a conventional finite-difference method and the Sinc method. The numerical results demonstrate that the new method is relatively accurate and easily implemented.

AB - In this paper, we apply a new decomposition scheme to solve the linear heat equation. The approach is based on the choice of a suitable differential operator which may be ordinary or partial, linear or nonlinear, deterministic or stochastic. It does not require discretization and consequently of massive computation. In this scheme the solution is performed in the form of a convergent power series with easily computable components. This paper is particularly concerned with the Adomian decomposition method and the results obtained are compared to those obtained by a conventional finite-difference method and the Sinc method. The numerical results demonstrate that the new method is relatively accurate and easily implemented.

KW - A parabolic partial differential equation

KW - Finite-difference method

KW - Sinc functions

KW - The Adomian decomposition method

UR - http://www.scopus.com/inward/record.url?scp=4544348370&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=4544348370&partnerID=8YFLogxK

U2 - 10.1016/j.amc.2003.08.079

DO - 10.1016/j.amc.2003.08.079

M3 - Article

AN - SCOPUS:4544348370

VL - 157

SP - 735

EP - 743

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

SN - 0096-3003

IS - 3

ER -