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020 _a9783031447846
_9978-3-031-44784-6
024 7 _a10.1007/978-3-031-44784-6
_2doi
050 4 _aTA329-348
050 4 _aTA345-345.5
072 7 _aTBJ
_2bicssc
072 7 _aTEC009000
_2bisacsh
072 7 _aTBJ
_2thema
100 1 _aVandandoo, Ulziibayar.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_970599
245 1 0 _aHigh-Order Finite Difference and Finite Element Methods for Solving Some Partial Differential Equations
_h[electronic resource] /
_cby Ulziibayar Vandandoo, Tugal Zhanlav, Ochbadrakh Chuluunbaatar, Alexander Gusev, Sergue Vinitsky, Galmandakh Chuluunbaatar.
250 _a1st ed. 2024.
264 1 _aCham :
_bSpringer Nature Switzerland :
_bImprint: Springer,
_c2024.
300 _aXIII, 114 p. 14 illus., 7 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aSynthesis Lectures on Engineering, Science, and Technology,
_x2690-0327
505 0 _aThe 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.
520 _aThis 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.
650 0 _aEngineering mathematics.
_964145
650 0 _aEngineering
_xData processing.
650 0 _aMathematics
_xData processing.
_965715
650 0 _aMechanics, Applied.
650 1 4 _aMathematical and Computational Engineering Applications.
650 2 4 _aComputational Science and Engineering.
_965717
650 2 4 _aEngineering Mechanics.
700 1 _aZhanlav, Tugal.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_970600
700 1 _aChuluunbaatar, Ochbadrakh.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_970601
700 1 _aGusev, Alexander.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_970602
700 1 _aVinitsky, Sergue.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_970603
700 1 _aChuluunbaatar, Galmandakh.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_970604
710 2 _aSpringerLink (Online service)
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9783031447839
776 0 8 _iPrinted edition:
_z9783031447853
776 0 8 _iPrinted edition:
_z9783031447860
830 0 _aSynthesis Lectures on Engineering, Science, and Technology,
_x2690-0327
856 4 0 _uhttps://doi.org/10.1007/978-3-031-44784-6
912 _aZDB-2-SXSC
999 _c57487
_d57487