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Numerical solution of the one‐dimensional heat equation on the bounded intervals using fundamental solutions
Author(s) -
Tatari Mehdi,
Dehghan Mehdi,
Razzaghi Mohsen
Publication year - 2008
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.20296
Subject(s) - mathematics , heat equation , bounded function , work (physics) , partial differential equation , stability (learning theory) , gravitational singularity , mathematical analysis , numerical stability , finite difference method , ftcs scheme , numerical analysis , differential equation , thermodynamics , computer science , ordinary differential equation , differential algebraic equation , physics , machine learning
We present a numerical method for the solution of heat equation with sufficiently smooth initial condition, using fundamental solutions of heat equation in terms of singularities. In this work various aspects of this method such as efficiency, stability, and convergency are given and a comparison with some well‐known finite difference methods will be obtained. Numerical results are reported to support the superiority of the developed method. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2008