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Difference Methods for PDE in Several Dimensions

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Abstract

The basic concepts of difference methods for PDE in several dimensions are readily adopted from the discussion of one-dimensional initial-boundary-value problems (Chap. 9). We are seeking consistent, stable difference schemes and corresponding discretizations of the initial and boundary conditions by which we obtain convergence of the numerical solution to the exact solution of the differential equation. Except in (10.21) and (10.22) we restrict the discussion to PDE with time dependence in two spatial coordinates.

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Authors and Affiliations

  1. Faculty of Mathematics and Physics, University of Ljubljana, Ljubljana, Slovenia

    Simon Širca & Martin Horvat

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  1. Simon Širca
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  2. Martin Horvat
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Correspondence to Simon Širca .

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Širca, S., Horvat, M. (2018). Difference Methods for PDE in Several Dimensions. In: Computational Methods in Physics. Graduate Texts in Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-78619-3_10

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