Abstract
This article aims to present a new approach based on C1 -cubic splines introduced by Sallam and Naim Anwar [Sallam, S. and Naim Anwar, M. (2000). Stabilized cubic C1-spline collocation method for solving first-order ordinary initial value problems, Int. J. Comput. Math., 74, 87-96.], which is A-stable, for the time integration of parabolic equations (diffusion or heat equation). The introduced method is an example of the so-called method of lines (the solution is thought to consist of space discretization and time integration), which is an extension of the 1/3-Simpson's finite-difference scheme. Our main objective is to prove the unconditional stability of the proposed method as well as to show that the method is convergent and is of order O(h2) + O(k4) i.e. it is a fourth-order in time and second-order in space. Computational results also show that the method is relevant for long time interval problems.
Original language | English |
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Pages (from-to) | 813-821 |
Number of pages | 9 |
Journal | International Journal of Computer Mathematics |
Volume | 81 |
Issue number | 7 |
DOIs | |
Publication status | Published - Jul 2004 |
Keywords
- Collocation methods
- Cubic splines
- Extended 1/3-Simpson's finite-difference scheme
- Method of lines
- Parabolic equations
- Unconditional stability
ASJC Scopus subject areas
- Computer Science Applications
- Computational Theory and Mathematics
- Applied Mathematics