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Accurate finite difference approximations for the solution of parabolic partial differential equations by semi‐discretization
Author(s) -
Huntley E.
Publication year - 1986
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620231213
Subject(s) - discretization , mathematics , boundary value problem , finite difference , partial differential equation , dirichlet boundary condition , homogeneous , dirichlet distribution , mathematical analysis , finite difference method , neumann boundary condition , simple (philosophy) , matrix (chemical analysis) , finite element method , philosophy , materials science , epistemology , combinatorics , composite material , physics , thermodynamics
The advantages in formulation and use of semi‐discretized approaches to the numerical solution of initial/boundary value problems are well known. The aim of this paper is to demonstrate that it is feasible to obtain accurate results even with a coarse spatial mesh. A method is developed which produces in a simple manner matrix representations for high‐order central difference operators. Dirichlet, Neumann and mixed boundary conditions are considered, both homogeneous and non‐homogeneous. It is shown in all cases that, for linear problems at least, there is no need to use a finer mesh than that dictated by the essential frequency content of the initial function data.