Multipoint problem for hyperbolic equations with variable coefficients

1996 ◽  
Vol 48 (11) ◽  
pp. 1659-1668 ◽  
Author(s):  
P. B. Vasylyshyn ◽  
I. S. Klyus ◽  
B. I. Ptashnyk
Keyword(s):  
Hyperbolic Equations ◽  
Variable Coefficients ◽  
Multipoint Problem

scholarly journals Finite Difference Method for Hyperbolic Equations with the Nonlocal Integral Condition

2011 ◽  
Vol 2011 ◽  
pp. 1-15 ◽  
Author(s):  
Allaberen Ashyralyev ◽  
Necmettin Aggez
Keyword(s):  
Space Variable ◽  
Hyperbolic Equations ◽  
Nonlocal Boundary ◽  
Integral Condition ◽  
Variable Coefficients ◽  
Difference Schemes ◽  
Order Difference ◽  
One Dimensional ◽  
Nonlocal Integral Condition ◽  
Multidimensional Hyperbolic Equations

The stable difference schemes for the approximate solution of the nonlocal boundary value problem for multidimensional hyperbolic equations with dependent in space variable coefficients are presented. Stability of these difference schemes and of the first- and second-order difference derivatives is obtained. The theoretical statements for the solution of these difference schemes for one-dimensional hyperbolic equations are supported by numerical examples.

scholarly journals STATICS AND DYNAMICS OF INTERACTION OF SOLID CONCRETIONS WITH GRANULAR MEDIUM

2019 ◽  
pp. 12-22 ◽  
Author(s):  
Olena Solona ◽  
Vladimir Kovbasa
Keyword(s):  
Mechanical Properties ◽  
Numerical Solution ◽  
Granular Medium ◽  
Granular Media ◽  
Hyperbolic Equations ◽  
Dynamic Effect ◽  
Variable Coefficients ◽  
Statics And Dynamics ◽  
Angular Displacements

This part of the article is a continuation of the first part of the article of the same name. The equations of boundary conditions, which are the displacements applied to the walls of the container are derived in this part. A system of hyperbolic equations with variable coefficients is obtained. It allows, together with the static equations given in Part 1, to obtain the values of the velocity components of the displacements of granular media in the container, as well as changes in its density, depending on the medium mechanical properties and the kinematic regimes of the applied displacements. The numerical solution of this system of equations allows one to solve successively the equations on the determination of stress components both in the wall layers and in the absence of the action of the walls of the container. The equations are given that allow us to determine the possible linear and angular displacements of concretions in the wall layers during the contact interaction of the concretion with the wall, and also in the absence of contact interactions taking into account the dynamic effect of the granular medium, that is moving. These functions are obtained for the most general cases, which include the granular medium's mechanical properties, the geometric dimensions, shapes and mechanical properties of the concretions and walls of the container, and the kinematic regimes of the impacts applied to the walls of the container. The equations obtained are the initial ones for the numerical solution of the problems of displacements, changes in the density of the granular medium, and the possible linear and angular displacements of concretions that are in the medium. Using finite elements method (FEM) or finite volumes method (DEM) it is possible to obtain final solutions of the equations. These equations make it possible to determine the kinematic regimes of the applied kinematic effects in order to obtain the necessary density changes and possible displacements of granular media, as well as the necessary displacements and velocities of these displacements concretions, which are in a moving granular medium.

A multipoint problem with multiple nodes for linear hyperbolic equations

1999 ◽  
Vol 51 (10) ◽  
pp. 1476-1483
Author(s):  
V. I. Bernik ◽  
V. V. Beresnevich ◽  
P. B. Vasylyshyn ◽  
B. I. Ptashnyk
Keyword(s):  
Hyperbolic Equations ◽  
Multipoint Problem ◽  
Linear Hyperbolic Equations
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