The development of jump discontinuities in nonlinear hyperbolic systems of equations in two independent variables

1963 ◽  
Vol 14 (1) ◽  
pp. 27-37 ◽  
Author(s):  
A. Jeffrey
Keyword(s):  
Hyperbolic Systems ◽  
Systems Of Equations ◽  
Independent Variables ◽  
Hyperbolic Systems Of Equations ◽  
Jump Discontinuities ◽  
Two Independent Variables ◽  
Nonlinear Hyperbolic Systems

scholarly journals Using the Sharp scheme of higher-order accuracy for solving some nonlinear hyperbolic systems of equations

2019 ◽  
pp. 45-53
Author(s):  
А.В. Соловьев ◽  
А.В. Данилин
Keyword(s):  
Difference Scheme ◽  
Hyperbolic Systems ◽  
Higher Order ◽  
Test Problems ◽  
Systems Of Equations ◽  
Order Accuracy ◽  
One Dimensional ◽  
Hyperbolic Systems Of Equations ◽  
Sharp Difference ◽  
Nonlinear Hyperbolic Systems

Разностная схема Диез повышенного порядка точности, ранее разработанная для решения скалярного одномерного уравнения переноса, с помощью балансно-характеристического подхода распространена на нелинейные системы уравнений мелкой воды и уравнений Эйлера. Для обеих систем уравнений решены тестовые задачи, иллюстрирующие особенности решений, полученных с помощью описываемой разностной схемы. The Sharp difference scheme of higher-order accuracy developed previously for solving the scalar one-dimensional transport equation is extended to the shallow water nonlinear systems and to the systems of Euler equations using the balance-characteristic approach. For these systems, a number of test problems are solved to illustrate the features of the solutions obtained by the described difference scheme.

scholarly journals Circular and transverse wave solutions of non-linear hyperbolic systems of equations

1968 ◽  
Vol 16 (2) ◽  
pp. 117-126
Author(s):  
Robin J. Waterston
Keyword(s):  
Hyperbolic Systems ◽  
Finite Elasticity ◽  
Linear Equations ◽  
Systems Of Equations ◽  
Transverse Waves ◽  
Hyperbolic Systems Of Equations ◽  
Wide Range ◽  
Non Linear ◽  
Physical Phenomena ◽  
Non Linear Equations

Circularly and transversely polarised (henceforth called circular and transverse) waves have been shown to occur as solutions of non-linear equations governing a wide range of physical phenomena, including finite elasticity (1), magnetohydrodynamics (2), and gyromagnetism (3), but only when the material properties of the medium are isotropic with respect to the direction of wave propagation. This paper is an attempt to unify and generalise these results.

scholarly journals On the differential equations of H. Lewy

1961 ◽  
Vol 2 (1) ◽  
pp. 11-16
Author(s):  
W. B. Smith-White
Keyword(s):  
Differential Equations ◽  
Special Form ◽  
Linear Equations ◽  
Systems Of Equations ◽  
Independent Variables ◽  
Image Position ◽  
Two Independent Variables

It is known that the theory of Cauchy's problem for differential equations with two independent variables is réducible to the corresponding problem for systems of quasi-linear equations. The reduction is carried further, by means of the theory of characteristics, to the case of systems of equations of the special form first considered by H. Lewy [1]. The simplest case is that of the pair of equationswhere the aii depend on z1 and z2. The problem to be considered is that of finding functions z1(x, y), z2(x, y) which satisfy (1) and which take prescribed values on x + y = 0.

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