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

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发表于 2025-3-21 17:04:01 | 显示全部楼层 |阅读模式
期刊全称Analysis of Approximation Methods for Differential and Integral Equations
影响因子2023H.-J. Reinhardt
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学科分类Applied Mathematical Sciences
图书封面Titlebook: Analysis of Approximation Methods for Differential and Integral Equations;  H.-J. Reinhardt Textbook 1985 Springer Science+Business Media N
影响因子This book is primarily based on the research done by the Numerical Analysis Group at the Goethe-Universitat in Frankfurt/Main, and on material presented in several graduate courses by the author between 1977 and 1981. It is hoped that the text will be useful for graduate students and for scientists interested in studying a fundamental theoretical analysis of numerical methods along with its application to the most diverse classes of differential and integral equations. The text treats numerous methods for approximating solutions of three classes of problems: (elliptic) boundary-value problems, (hyperbolic and parabolic) initial value problems in partial differential equations, and integral equations of the second kind. The aim is to develop a unifying convergence theory, and thereby prove the convergence of, as well as provide error estimates for, the approximations generated by specific numerical methods. The schemes for numerically solving boundary-value problems are additionally divided into the two categories of finite­ difference methods and of projection methods for approximating their variational formulations.
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发表于 2025-3-21 23:51:07 | 显示全部楼层
Alexander Mertes,Florian Liberatorerry out this analysis for both linear and nonlinear problems. As preparation, we give some general results on the solvability of linear equations of the second kind and apply these to integral equations.
发表于 2025-3-22 04:15:58 | 显示全部楼层
Max Schröder,Sebastian Bader,Thomas Kirste convergence “discretely uniform convergence”, but we wish to point out that this convergence is nothing other than discrete convergence in the sense of Section 5.1 with respect to a particular norm. In Section 5.4, we explore the concept of discrete convergence further by considering the example of
发表于 2025-3-22 05:31:42 | 显示全部楼层
Sabine Hahn,Friederike J. S. Thilo). By virtue of the characterizations of stability to be discussed in Section 6.2, we are able to obtain equivalent conditions for the discrete convergence of differentiable mappings, along with error estimates (cf. Theorem 6.14). The concluding Section 6.4 establishes and characterizes the discrete
发表于 2025-3-22 12:08:37 | 显示全部楼层
Michael Prilla,Heinrich Recken,Marc JanßenGalerkin methods, we aim to produce quasi-optimal error estimates with respect to the approximations in the spatial variable. Attaining such estimates requires extensive investigations for rather simple problems so that we shall necessarily restrict the scope of our analysis of Galerkin methods to a
发表于 2025-3-22 14:04:09 | 显示全部楼层
Analysis of Approximation Methods for Differential and Integral Equations
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发表于 2025-3-23 05:02:13 | 显示全部楼层
Projection Methods for Variational Equationsdering and solving each problem in a finite-dimensional subspace of the respective Hilbert spaces obtained in Section 2.2. This procedure can be viewed as a projection method. Among the many special types of projection methods in this chapter, Ritz-Galerkin methods are used for approximating solutio
发表于 2025-3-23 05:48:19 | 显示全部楼层
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