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

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Max Schröder,Sebastian Bader,Thomas Kirsteore precise in a general setting. These concepts are introduced in Section 5.1, and explained by means of introductory examples. In Section 5.2, we show how discrete approximations are constructed by restriction and imbedding operators. On the other hand, we demonstrate that restriction operators ca

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Sabine Hahn,Friederike J. S. Thiloprepare 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

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Arne Buss,Pavo Marijic,Steve Strupeit, regularly convergent, and discretely compact operator sequences. These properties provide criteria for inverse stability (respectively, bistability) which, as we know from the theory developed in the preceding chapter, are essential for deducing the inverse discrete convergence (respectively, bico

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https://doi.org/10.1007/978-3-658-23987-9we study the convergence of finite-difference approximations to both linear and nonlinear ordinary differential equations of second order and to Poisson’s equation on a rectangle. In Chapter 1, appropriate finite-difference approximations were introduced, and both the exact and the approximate equat

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Marc Kraft,Susanne Dannehl,Thomas Schaueranner, we were able to apply projection methods to nonlinear problems. The prototype examples for illustrating our methods were examples of boundary-value problems in ordinary and partial differential equations already introduced in Chapter 1; the convergence analysis for the finite-difference appro

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https://doi.org/10.1007/978-3-658-25461-2 that such problems are pure initial value problems, and allow that the mappings occurring in both the exact formulation of the problem, and in the associated approximations, depend on time. Our convergence theory established for the problems in this chapter will essentially consist of a rather conc

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https://doi.org/10.1007/978-3-658-25461-2riteria strongly depend on the norms of the approximating spaces. The significance of the choice of norms was already made clear in Section 11.1 where we verified the differentiability requirements for several classes of examples. The analysis in this chapter, moreover, is applicable to nonlinear pr

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