UID:
almahu_9949744360402882
Format:
XIII, 114 p. 14 illus., 7 illus. in color.
,
online resource.
Edition:
1st ed. 2024.
ISBN:
9783031447846
Series Statement:
Synthesis Lectures on Engineering, Science, and Technology,
Content:
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.
Note:
The accurate finite-difference scheme for the Helmholtz and wave equations -- Higher-order accurate finite-difference schemes for the Burgers' equations -- High-accuracy finite element method schemes for solution of discrete spectrum problems -- References -- Appendices.
In:
Springer Nature eBook
Additional Edition:
Printed edition: ISBN 9783031447839
Additional Edition:
Printed edition: ISBN 9783031447853
Additional Edition:
Printed edition: ISBN 9783031447860
Language:
English
DOI:
10.1007/978-3-031-44784-6
URL:
https://doi.org/10.1007/978-3-031-44784-6
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