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A consistent and accurate procedure for obtaining difference equations from differential equations
Author(s) -
Lick Wilbert,
Gaskins Tom
Publication year - 1984
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.1620200807
Subject(s) - mathematics , differential equation , mathematical analysis , boundary value problem , finite difference method , extension (predicate logic) , numerical partial differential equations , series (stratigraphy) , computer science , programming language , paleontology , biology
A general, consistent and accurate procedure for obtaining difference equations from differential equations is presented and illustrated by several examples. The procedure is an extension of the integral method and incorporates what is known of the solution to the differential equation in the formation of the corresponding difference equation. For the same accuracy, large increases in grid size over that obtained by standard Taylor's series approximations are possible. Both boundary‐value and initial‐value problems are treated.