High-Order Finite Difference and Finite Element Methods for Solving Some Partial Differential Equations
Vandandoo, Ulziibayar.
creator
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Zhanlav, Tugal.
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Chuluunbaatar, Ochbadrakh.
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http://id.loc.gov/vocabulary/relators/aut
Gusev, Alexander.
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Vinitsky, Sergue.
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Chuluunbaatar, Galmandakh.
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http://id.loc.gov/vocabulary/relators/aut
SpringerLink (Online service)
text
sz
2024
1st ed. 2024.
monographic
eng
access
XIII, 114 p. 14 illus., 7 illus. in color. online resource.
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.
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.
by Ulziibayar Vandandoo, Tugal Zhanlav, Ochbadrakh Chuluunbaatar, Alexander Gusev, Sergue Vinitsky, Galmandakh Chuluunbaatar.
Engineering mathematics
Engineering
Data processing
Mathematics
Data processing
Mechanics, Applied
Mathematical and Computational Engineering Applications
Computational Science and Engineering
Engineering Mechanics
TA329-348
TA345-345.5
Springer Nature eBook
Synthesis Lectures on Engineering, Science, and Technology
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https://doi.org/10.1007/978-3-031-44784-6
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