The Accurate Finite-difference Scheme and Finite-element Method for some Partial Differential Equations
Language: English
Published by Springer Nature Switzerland, 2024
Series: Book 84 of 110 - Synthesis Lectures on Engineering, Science, and Technology
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Condition: New
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Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. Deals with accurate numerical schemesDescribes new methodsTreatment of multidimensional boundary value problemsThis monograph is intended for graduate students, researchers and teachers. It is devoted to the construction of high-.
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- Title
- The Accurate Finite-difference Scheme and Finite-element Method for some Partial Differential Equations
- Author
- Ulziibayar Vandandoo|Tugal Zhanlav|Ochbadrakh Chuluunbaatar|Alexander Gusev|Sergue Vinitsky|Galmandakh Chuluunbaatar
- Publisher
- Springer Nature Switzerland
- Publication year
- 2024
- Condition
- New
- Binding
- Gebunden
- Language
- English
- ISBN 10
- 3031447832
- ISBN 13
- 9783031447839
- Series
- Book 84 of 110: Synthesis Lectures on Engineering, Science, and Technology
The monograph is devoted to the construction of the high-order finite difference and finite element methods for numerical solving multidimensional boundary-value problems (BVPs) for different partial differential equations, in particular, linear Helmholtz and wave equations, nonlinear Burgers’ equations, and elliptic (Schrödinger) equation. Despite of a long history especially in development of the theoretical background of these methods there are open questions in their constructive implementation in numerical solving the multidimensional BVPs having additional requirement on physical parameters or desirable properties of its approximate solutions.
Over the last two decades many papers on this topics have been published, in which new constructive approaches to numerically solving the multidimensional BVPs were proposed, and its highly desirable to systematically collect these results. This motivate us to write thus monograph based on our research results obtainedin collaboration with the co-authors. Since the topic is importance we believe that this book will be useful to readers, graduate students and researchers interested in the field of computational physics, applied mathematics, numerical analysis and applied sciences
"Synopsis" may belong to another edition of this title.
From the Back Cover
This monograph is intended for graduate students, researchers and teachers. It is devoted to the construction of high-order schemes of the finite difference method and the finite element method for the solution of multidimensional boundary value problems for various partial differential equations, in particular, linear Helmholtz and wave equations, and nonlinear Burgers' equation. The finite difference method is a standard numerical method for solving boundary value problems. Recently, considerable attention has been paid to constructing an accurate (or exact) difference approximation for some ordinary and partial differential equations. An exact finite difference method is developed for Helmholtz and wave equations with general boundary conditions (including initial condition for wave equation) on the rectangular domain in R2. The method proposed here comes from [4] and is based on separation of variables method and expansion of one-dimensional three-point difference operators forsufficiently smooth solution. The efficiency and accuracy of the method have been tested on several examples.
"About the title" may belong to another edition of this title.
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