Abstract
Given the PDE
where P is a differential operator in space, one can first discretize in space and obtain a system of ODE
Here ν is a grid function, and Q is a difference operator. This is called a semidiscrete approximation, or the method of lines. The latter name originates from the graph in the x/t plane, where the discretization is shown by vertical, but continuous lines. It is assumed that the system (4.1) is solved by some standard method in time. In the following we shall discuss the derivation of different types of operators Q.
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© 2008 Springer-Verlag Berlin Heidelberg
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(2008). Approximation in Space. In: High Order Difference Methods for Time Dependent PDE. Springer Series in Computational Mathematics, vol 38. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74993-6_4
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DOI: https://doi.org/10.1007/978-3-540-74993-6_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-74992-9
Online ISBN: 978-3-540-74993-6
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