The accurate finite-difference scheme and finite-element method for some partial differential equations

Ulziibayar Vandondoo, Tugal Zhanlav, Ochbadrakh Chuluunbaatar (Autoren)

Buch | Hardcover

XVII, 106 Seiten

2024 | 1. Auflage
Springer International Publishing (Verlag)
978-3-031-44783-9 (ISBN)

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lt;p>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 for sufficiently 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.

Erscheinungsdatum	07.02.2024
Reihe/Serie	Synthesis Lectures on Engineering, Science, and Technology
Zusatzinfo	Illustrationen
Verlagsort	Cham
Sprache	englisch
Maße	168 x 240 mm
Gewicht	385 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
	Technik ► Maschinenbau
Schlagworte	boundary value problems • Burgers´ equation • Helmholtz equation • Newton´s method • numerical solution • partial differential equation
ISBN-10	3-031-44783-2 / 3031447832
ISBN-13	978-3-031-44783-9 / 9783031447839
Zustand	Neuware