Abstract
Finite difference methods were used for solving differential equations long before computers were available. As we have seen in Chap. 2, these methods arise quite naturally by going back to the definition of derivatives, and just stopping short of taking the limit as the step size tends to zero. It is still a major class of methods, and for initial value problems for ordinary differential equations it is still the dominating technique. However, in order to be effective for partial differential equations, difference methods require structured grids, and for many applications it is difficult to construct such grids.
We shall first discuss ordinary differential equations and then partial differential equations.
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© 2011 Springer-Verlag Berlin Heidelberg
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Gustafsson, B. (2011). Finite Difference Methods. In: Fundamentals of Scientific Computing. Texts in Computational Science and Engineering, vol 8. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-19495-5_10
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DOI: https://doi.org/10.1007/978-3-642-19495-5_10
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-19494-8
Online ISBN: 978-3-642-19495-5
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