04093nam a22006015i 4500 978-3-031-44784-6 DE-He213 20251030111416.0 cr nn 008mamaa 240205s2024 sz | s |||| 0|eng d 9783031447846 978-3-031-44784-6 10.1007/978-3-031-44784-6 doi TA329-348 TA345-345.5 TBJ bicssc TEC009000 bisacsh TBJ thema Vandandoo, Ulziibayar. author. aut http://id.loc.gov/vocabulary/relators/aut 70599 High-Order Finite Difference and Finite Element Methods for Solving Some Partial Differential Equations [electronic resource] / by Ulziibayar Vandandoo, Tugal Zhanlav, Ochbadrakh Chuluunbaatar, Alexander Gusev, Sergue Vinitsky, Galmandakh Chuluunbaatar. 1st ed. 2024. Cham : Springer Nature Switzerland : Imprint: Springer, 2024. XIII, 114 p. 14 illus., 7 illus. in color. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Synthesis Lectures on Engineering, Science, and Technology, 2690-0327 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. 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. Engineering mathematics. 64145 Engineering Data processing. Mathematics Data processing. 65715 Mechanics, Applied. Mathematical and Computational Engineering Applications. Computational Science and Engineering. 65717 Engineering Mechanics. Zhanlav, Tugal. author. aut http://id.loc.gov/vocabulary/relators/aut 70600 Chuluunbaatar, Ochbadrakh. author. aut http://id.loc.gov/vocabulary/relators/aut 70601 Gusev, Alexander. author. aut http://id.loc.gov/vocabulary/relators/aut 70602 Vinitsky, Sergue. author. aut http://id.loc.gov/vocabulary/relators/aut 70603 Chuluunbaatar, Galmandakh. author. aut http://id.loc.gov/vocabulary/relators/aut 70604 SpringerLink (Online service) Springer Nature eBook Printed edition: 9783031447839 Printed edition: 9783031447853 Printed edition: 9783031447860 Synthesis Lectures on Engineering, Science, and Technology, 2690-0327 https://doi.org/10.1007/978-3-031-44784-6 ZDB-2-SXSC 57487 57487