THERMAL SCIENCE

International Scientific Journal

Authors of this Paper

External Links

Yulan Wang

,

Dan Tian

,

Zhiyuan Li

NUMERICAL METHOD FOR SINGULARLY PERTURBED DELAY PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS

ABSTRACT
The barycentric interpolation collocation method(BICM) is discussed in this paper, which is not valid for singularly perturbed delay partial differential equations. A modified version is proposed to overcome this disadvantage. Two numerical examples are provided to show the effectiveness of the present method.
KEYWORDS
barycentric interpolation, singularly perturbed, delay parameter, Chebyshev nodes, Taylor’s series expansion
PAPER SUBMITTED: 2016-06-15
PAPER REVISED: 2016-08-04
PAPER ACCEPTED: 2016-09-04
PUBLISHED ONLINE: 2017-09-09
DOI REFERENCE: https://doi.org/10.2298/TSCI160615040W
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2017, VOLUME 21, ISSUE Issue 4, PAGES [1595 - 1599]
REFERENCES
  1. Ansari, A. R., A Parameter-Robust Finite Difference Method for Singularly Perturbed Delay Parabolic Partial Differential Equations, Applied Mathematics and Computation, 205 (2007), 1, pp. 552-566
  2. Berrut, J. P., Trefethen, L. N., Barycentric Lagrange Interpolation, SIAM Review, 46 (2004), 3, pp. 501-517
  3. Berrut, J. P., Linear Rational Interpolation and Its Applications in Approximate and Boundary Value Problems, Journal of Mathematics, 31 (2002), 2, pp. 997-1002
  4. Kumar, S., Kumar, M., High Order Parameter-Uniform Discretization for Singularly Perturbed Parabolic Partial Differential Equations with Time Delay, Applied Mathematics and Computation, 68 (2014), 10, pp. 1355-1367
  5. Ansari, A. R., A Parameter-Robust Finite Difference Method for Singularly Perturbed Delay Parabolic Partial Differential Equations, Journal of Computational and Applied Mathematics, 205 (2007), 1, pp. 552-566
  6. Bashier, E. B. M., Patidar, K. C. A Novel fitted Operator Finite Difference Method for a Singularly Perturbed Delay Parabolic Partial Differential Equation, Applied Mathematics and Computation, 217 (2011), 9, pp. 4728-4739
  7. Salkuyeh, D. K., Tavakoli, A., Interpolated Variational Iteration Method for Initial Value Problems, Applied Mathematical Modelling, 40 (2016), 5, pp. 3979-3990
  8. Siddiqi, S., Iftikhar, M., Variational Iteration Method for the Solution of Seventh Order Boundary Value Problems Using He's Polynomials, Journal of the Association of Arab Universities for Basic and Applied Sciences, 18 (2015), 1, pp. 60-65
  9. Nazari, G. A., A Modified Homotopy Perturbation Method Coupled with the Fourier Transform for Nonlinear and Singular Lane-Emden Equations, Applied Mathematics Letters, 26 (2013), 10, pp. 1018-1025
PDF VERSION [DOWNLOAD]
Numerical method for singularly perturbed delay parabolic partial differential equations

© 2024 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence