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Difference Equations from Differential Equations (Paperback, Softcover reprint of the original 1st ed. 1989)
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Difference Equations from Differential Equations (Paperback, Softcover reprint of the original 1st ed. 1989)
Series: Lecture Notes in Engineering, 41
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In computational mechanics, the first and quite often the most
difficult part of a problem is the correct formulation of the
problem. This is usually done in terms of differential equations.
Once this formulation is accomplished, the translation of the
governing differential equations into accurate, stable, and
physically realistic difference equations can be a formidable task.
By comparison, the numerical evaluation of these difference
equations in order to obtain a solution is usually much simpler.
The present notes are primarily concerned with the second task,
that of deriving accurate, stable, and physically realistic
difference equations from the governing differential equations.
Procedures for the numerical evaluation of these difference
equations are also presented. In later applications, the physical
formulation of the problem and the properties of the numerical
solution, especially as they are related to the numerical
approximations inherent in the solution, are discussed. There are
numerous ways to form difference equations from differential
equations.
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