Computational methods for delay parabolic and time‐fractional partial differential equations
- 11 August 2009
- journal article
- research article
- Published by Wiley in Numerical Methods for Partial Differential Equations
- Vol. 26 (6) , 1556-1571
Abstract
This article is concerned with ϑ‐methods for delay parabolic partial differential equations. The methodology is extended to time‐fractional‐order parabolic partial differential equations in the sense of Caputo. The fully implicit scheme preserves delay‐independent asymptotic stability and the solution continuously depends on the time‐fractional order. Several numerical examples of interest are included to demonstrate the effectiveness of the method. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2010Keywords
This publication has 18 references indexed in Scilit:
- Open issues in devising software for the numerical solution of implicit delay differential equationsJournal of Computational and Applied Mathematics, 2006
- The Effects of Temporal Delays in a Model for a Food-Limited, Diffusing PopulationJournal of Mathematical Analysis and Applications, 2001
- Implementing Radau IIA Methods for Stiff Delay Differential EquationsComputing, 2001
- Dynamics of constant and variable stepsize methods for a nonlinear population model with delayApplied Numerical Mathematics, 1997
- The Stability of the θ-methods in the Numerical Solution of Delay Differential EquationsIMA Journal of Numerical Analysis, 1990
- Stability of numerical methods for delay differential equationsJournal of Computational and Applied Mathematics, 1989
- An Abstract Delay-Differential Equation Modelling Size Dependent Cell Growth and DivisionSIAM Journal on Mathematical Analysis, 1987
- Some aspects of the boundary locus methodBIT Numerical Mathematics, 1980
- Spatial structures in predator-prey communities with hereditary effects and diffusionMathematical Biosciences, 1979
- On the computational solution of a class of functional differential equationsJournal of Mathematical Analysis and Applications, 1965