A PARAMETRIC DIFFERENCE SCHEME FOR THE NUMERICAL SOLUTION OF A MIXED PROBLEM FOR A WAVE EQUATION IN A REGION WITH AN ANGLE

2020 ◽  
Vol 2 (1) ◽  
pp. 38-43
Author(s):  
Shafoat Imomova ◽  
Keyword(s):  
Wave Equation ◽  
Difference Scheme ◽  
Numerical Solution ◽  
Mixed Problem

scholarly journals New high-order conservative difference scheme for regularized long wave equation with Richardson extrapolation

2019 ◽  
Vol 23 (Suppl. 3) ◽  
pp. 737-745
Author(s):  
Jin-Song Hu ◽  
Jia-Jia Li ◽  
Xi Wang
Keyword(s):  
Wave Equation ◽  
Difference Scheme ◽  
Numerical Solution ◽  
Richardson Extrapolation ◽  
Discrete Energy ◽  
Linear System Of Equations ◽  
Long Wave ◽  
Implicit Finite Difference Scheme ◽  
Regularized Long Wave Equation ◽  
Discrete Mass

Numerical solution for the regularized long wave equation is considered by a new three-level conservative implicit finite difference scheme coupled with Richardson extrapolation which has the accuracy of O(? + h4). The scheme is a linear system of equations solved without iteratio. The conservation properties of the algorithm are verified by computing the discrete mass and discrete energy. Existence and uniqueness of the numerical solution are proved. Convergence and stability of the scheme are also derived using energy method. The results of numerical experiments show that our proposed scheme is efficiency.

Classical and generalized of a mixed problem– solutions for a non-homogeneous wave equation

2019 ◽  
Vol 484 (1) ◽  
pp. 18-20
Author(s):  
A. P. Khromov ◽  
V. V. Kornev
Keyword(s):  
Wave Equation ◽  
Fourier Series ◽  
Mixed Problem ◽  
Homogeneous Equation ◽  
Generalized Solution ◽  
Problem Solution ◽  
Homogeneous Wave ◽  
Homogeneous Wave Equation ◽  
Explicit Expressions

This study follows A.N. Krylov’s recommendations on accelerating the convergence of the Fourier series, to obtain explicit expressions of the classical mixed problem–solution for a non-homogeneous equation and explicit expressions of the generalized solution in the case of arbitrary summable functions q(x), ϕ(x), y(x), f(x, t).

scholarly journals Сlassical solution of the mixed problem for the one-dimensional wave equation with the nonsmooth second initial condition

2020 ◽  
Vol 64 (6) ◽  
pp. 657-662
Author(s):  
V. I. Korzyuk ◽  
J. V. Rudzko
Keyword(s):  
Boundary Condition ◽  
Wave Equation ◽  
Mixed Problem ◽  
Method Of Characteristics ◽  
Smooth Boundary ◽  
Analytical Form ◽  
Initial Condition ◽  
One Dimensional ◽  
The One ◽  
Dimensional Wave

In this article, we study the classical solution of the mixed problem in a quarter of a plane and a half-plane for a one-dimensional wave equation. On the bottom of the boundary, Cauchy conditions are specified, and the second of them has a discontinuity of the first kind at one point. Smooth boundary condition is set at the side boundary. The solution is built using the method of characteristics in an explicit analytical form. Uniqueness is proved and conditions are established under which a piecewise-smooth solution exists. The problem with linking conditions is considered.

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