Titlebook: Analysis of Approximation Methods for Differential and Integral Equations; H.-J. Reinhardt Textbook 1985 Springer Science+Business Media N

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Analysis of Approximation Methods for Differential and Integral Equations978-1-4612-1080-1Series ISSN 0066-5452 Series E-ISSN 2196-968X

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Projection Methods for Variational Equationsons. In Section 2.1, we establish the relation between a linear operator equation and the associated variational formulation whenever the underlying linear space is a prehilbert space and then derive variational formulations in detail for each of the sample problems in Section 1.1. In order to deduc

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Approximation Methods for Integral Equations of the Second Kindded into two classes: the first class consists of those methods whose approximate equations are also expressible as integral equations with the regions of integration, measures, and kernels perturbed from the corresponding quantities in the original equation. In particular, this class includes quadr

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Approximation Methods for Initial Value Problems in Partial Differential Equations), which are typical examples of parabolic and hyperbolic problems, respectively. The methods we discuss comprise not only finite-difference methods but also Galerkin methods; our methods are either explicit or implicit and include so-called multilevel (more precisely, three-level) methods. In Secti

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Discrete Convergence of Mappings and Solutions of Equationsprepare the reader for the analysis in this chapter, we examine in Section 6.1 the relationship between the continuity of a mapping on the one hand and the differentiability and boundedness of its derivatives on the other. The most important result in 6.1 is a quantitative formulation of the Inverse