L-Stable Block Backward Differentiation Formula for Parabolic Partial Differential Equations

L-Stable Block Backward Differentiation Formula for Parabolic Partial Differential Equations

In this paper, an L-stable Second Derivative Block Backward Differentiation Formula (SDBBDF) of order 5 is presented for the solutions of parabolic equations. It applied the use of the classical method of lines for the discretization of the parabolic equations. The method reduces the one-dimensional...

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Bibliographic Details
Main Authors: B.I. Akinnukawe, O.A. Akinfenwa, S.A. Okunuga
Format: Article
Language:English
Published: Elsevier 2016-06-01
Series:Ain Shams Engineering Journal
Subjects:
Parabolic equation
Method of lines
L-stability
Second Derivative Block Backward Differentiation Formula
Online Access:http://www.sciencedirect.com/science/article/pii/S2090447916000228
Description
Summary:In this paper, an L-stable Second Derivative Block Backward Differentiation Formula (SDBBDF) of order 5 is presented for the solutions of parabolic equations. It applied the use of the classical method of lines for the discretization of the parabolic equations. The method reduces the one-dimensional parabolic partial differential equation which has integral or non-integral boundary conditions to a system of Ordinary Differential Equations (ODEs) with initial conditions. The stability properties of the block method are investigated using the boundary locus plot and the method was found to be L-stable. The derived method is implemented on standard problems of parabolic equations and the results obtained show that the method is accurate and efficient.
ISSN:2090-4479

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