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High-Order Finite Difference and Finite Element Methods for Solving Some Partial Differential Equations de Ulziibayar Vandandoo

High-Order Finite Difference and Finite Element Methods for Solving Some Partial Differential Equations: Synthesis Lectures on Engineering, Science, and Technology

Autor Ulziibayar Vandandoo, Tugal Zhanlav, Ochbadrakh Chuluunbaatar, Alexander Gusev, Sergue Vinitsky, Galmandakh Chuluunbaatar
en Limba Engleză Paperback – 23 feb 2025
The monograph is devoted to the construction of the high-order finite difference and finite element methods for numerical solving multidimensional boundary-value problems (BVPs) for different partial differential equations, in particular, linear Helmholtz and wave equations, nonlinear Burgers’ equations, and elliptic (Schrödinger) equation.
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Specificații

ISBN-13: 9783031447860
ISBN-10: 3031447867
Pagini: 128
Dimensiuni: 168 x 240 x 8 mm
Greutate: 0.23 kg
Editura: Springer
Seria Synthesis Lectures on Engineering, Science, and Technology

Cuprins

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.

Textul de pe ultima copertă

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.

Caracteristici

Deals with accurate numerical schemes Describes new methods Treatment of multidimensional boundary value problems