High-order accurate monotone compact running scheme for multidimensional hyperbolic equations

2015 ◽  
Vol 93 ◽  
pp. 150-163 ◽  
Author(s):  
A.V. Chikitkin ◽  
B.V. Rogov ◽  
S.V. Utyuzhnikov
Keyword(s):  
Hyperbolic Equations ◽  
High Order ◽  
Multidimensional Hyperbolic Equations

Fast high order ADER schemes for linear hyperbolic equations

2004 ◽  
Vol 197 (2) ◽  
pp. 532-539 ◽  
Author(s):  
Thomas Schwartzkopff ◽  
Michael Dumbser ◽  
Claus-Dieter Munz
Keyword(s):  
Hyperbolic Equations ◽  
High Order ◽  
Linear Hyperbolic Equations

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 Non-local problem with integral conditions for the three-dimensional high order hyperbolic equations

2020 ◽  
pp. 51-62
Author(s):  
Ш.Ш. Юсубов
Keyword(s):  
Integral Equation ◽  
Hyperbolic Equation ◽  
Hyperbolic Equations ◽  
Three Dimensional ◽  
High Order ◽  
Mixed Derivative ◽  
Local Problem ◽  
Integral Conditions ◽  
Order Hyperbolic Equation ◽  
Non Local

В работе для трехмерного гиперболического уравнения высокого порядка с доминирующей смешанной производной исследуется разрешимость нелокальной задачи с интегральными условиями. Поставленная задача сводится к интегральному уравнению и с помощью априорных оценок доказывается существование единственного решения. In the work the solvability of the non-local problem with integral conditions is investigated for the three-dimensional high order hyperbolic equation with dominated mixed derivative. The problem is reduced to the integral equation and existence of the solution is proved by the help of aprior estimations.

scholarly journals High order accurate two-step approximations for hyperbolic equations

1979 ◽  
Vol 13 (3) ◽  
pp. 201-226 ◽  
Author(s):  
Garth A. Baker ◽  
Vassilios A. Dougalis ◽  
Steven M. Serbin
Keyword(s):  
Hyperbolic Equations ◽  
High Order

scholarly journals The Inverse Problem for a General Class of Multidimensional Hyperbolic Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-11
Author(s):  
Gani Aldashev ◽  
Serik A. Aldashev
Keyword(s):  
Inverse Problem ◽  
General Class ◽  
Hyperbolic Equations ◽  
Existence Of Solution ◽  
Geophysical Prospecting ◽  
Hyperbolic Pde ◽  
Right Hand ◽  
Fourier Series Method ◽  
The Right ◽  
Multidimensional Hyperbolic Equations

Inverse problems for hyperbolic equations are found in geophysical prospecting and seismology, and their multidimensional analogues are especially important for applied work. However, whereas results have been established for the some narrow classes of hyperbolic equations, no results exist for more general classes. This paper proves the solvability of the inverse problem for a general class of multidimensional hyperbolic equations. Our approach consists of properly choosing the shape of the overidentifying condition that is needed to determine the right-hand side of the hyperbolic PDE and then applying the Fourier series method. We are then able to establish the results of the existence of solution for the cases when the unknown right-hand side is time- independent or space independent.

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