scholarly journals A High Order Accurate Finite Difference Method for the Drinfel’d–Sokolov–Wilson Equation

2021 ◽  
Vol 88 (1) ◽  
Author(s):  
Ludvig Lindeberg ◽  
Tuan Dao ◽  
Ken Mattsson
Keyword(s):  
Numerical Analysis ◽  
Finite Difference Method ◽  
Simultaneous Approximation ◽  
Vries Equation ◽  
Periodic Problem ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Wilson Equation ◽  
Simultaneous Approximation Term ◽  
Initial Boundary Value

AbstractWe analyse numerically the periodic problem and the initial boundary value problem of the Korteweg-de Vries equation and the Drindfeld–Sokolov–Wilson equation using the summation-by-parts simultaneous-approximation-term method. Two sets of boundary conditions are derived for each equation of which stability is shown using the energy method. Numerical analysis is done when the solution interacts with the boundaries. Results show the benefit of higher order SBP operators.

NUMERICAL ANALYSIS OF THE FINITE ELEMENT METHOD APPLIED TO THE BOLTZMANN-POISSON SYSTEM

1995 ◽  
Vol 05 (03) ◽  
pp. 351-365 ◽  
Author(s):  
V. SHUTYAEV ◽  
O. TRUFANOV
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Analysis ◽  
Semiconductor Device ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Poisson System ◽  
The Finite Element Method ◽  
Initial Boundary Value ◽  
Element Method

This paper is concerned with the numerical analysis of the mathematical model for a semiconductor device with the use of the Boltzmann equation. A mixed initial-boundary value problem for nonstationary Boltzmann-Poisson system in the case of one spatial variable is considered. A numerical algorithm for solving this problem is constructed and justified. The algorithm is based on an iterative process and the finite element method. A numerical example is presented.

scholarly journals Method of functional parametrization for solving a semi-periodic initial problem for fourth-order partial differential equations

2020 ◽  
Vol 100 (4) ◽  
pp. 5-16
Author(s):  
A.T. Assanova ◽  
◽  
Zh.S. Tokmurzin ◽  
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Fourth Order ◽  
Periodic Problem ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Hyperbolic Type ◽  
Order System ◽  
Partial Differential ◽  
Initial Boundary Value

A semi-periodic initial boundary-value problem for a fourth-order system of partial differential equations is considered. Using the method of functional parametrization, an additional parameter is carried out and the studied problem is reduced to the equivalent semi-periodic problem for a system of integro-differential equations of hyperbolic type second order with functional parameters and integral relations. An interrelation between the semi-periodic problem for the system of integro-differential equations of hyperbolic type and a family of Cauchy problems for a system of ordinary differential equations is established. Algorithms for finding of solutions to an equivalent problem are constructed and their convergence is proved. Sufficient conditions of a unique solvability to the semi-periodic initial boundary value problem for the fourth-order system of partial differential equations are obtained.

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