| 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 (h 2)?+?O (k 4) 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. |
