Unconditionally stable C1-cubic spline collocation method for solving parabolic equations

S. Sallam, M. Naim Anwar, M. R. Abdel-Aziz

Research output: Contribution to journalArticlepeer-review

14 Citations (Scopus)


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 languageEnglish
Pages (from-to)813-821
Number of pages9
JournalInternational Journal of Computer Mathematics
Issue number7
Publication statusPublished - Jul 2004


  • 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


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