Stable second-order finite-difference methods for linear initial-boundary-value problems

Finite-difference methods of second order at the boundary points are presented for problems with one-dimensional second-order hyperbolic and parabolic equations with mixed boundary conditions. These methods do not require information at points outside the region of consideration. The linear stabilit...

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Bibliographic Details
Published in:Applied mathematics letters Vol. 19; no. 2; pp. 146 - 154
Main Authors: George, K., Twizell, E.H.
Format: Journal Article
Language:English
Published: Oxford Elsevier Ltd 01.02.2006
Elsevier
Subjects:
Exact sciences and technology
Finite-difference methods
Mathematical analysis
Mathematics
Mixed boundary conditions
Numerical analysis
Numerical analysis. Scientific computation
Partial differential equations
Partial differential equations, boundary value problems
Partial differential equations, initial value problems and time-dependant initial-boundary value problems
Sciences and techniques of general use
Stability
Mixed boundary conditions
Stability
Finite-difference methods
Second order equation
Initial value problem
Crank Nicolson method
Parabolic equation
Boundary value problem
Numerical computation
Applied mathematics
Hyperbolic equation
Region
Potential method
Finite difference method
ISSN:0893-9659, 1873-5452
Online Access:Get full text
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Summary:Finite-difference methods of second order at the boundary points are presented for problems with one-dimensional second-order hyperbolic and parabolic equations with mixed boundary conditions. These methods do not require information at points outside the region of consideration. The linear stability of the algorithms developed is investigated. Numerical experiments are given for illustrating the accuracy and stability of the methods. Though the focus is on homogeneous boundary conditions, finite-difference methods with non-homogeneous mixed boundary conditions are also developed. To show the potential of the methods developed, in terms of CPU time, a comparison is made with the Crank–Nicolson method.
ISSN:0893-9659
1873-5452
DOI:10.1016/j.aml.2005.04.003