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Mixed problem for hyperbolic equation of second order

Mixed problem for hyperbolic equation of second order
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PARALLEL ALGORITHMS FOR SECOND-ORDER HYPERBOLIC EQUATIONS

Parallel Algorithms and Applications, 1995
Parallel algorithms are developed for the numerical solution of second-order hyperbolic partial differential equations using (M,K) Pade approximants with M ≠ K. A linear one-dimensional wave equation is solved using the algorithms and comparisons are made with results from the literature confirming the accuracy of the algorithms.
M. A. Arigu, Edward H. Twizell, Abba B. Gumel   +2 more
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Second Order Hyperbolic Equations with Small Nonlinearities

SIAM Journal on Applied Mathematics, 1978
A second order partial differential equation which describes the propagation of one-dimensional nonlinear waves in a bounded, inhomogeneous, dissipative medium is analyzed using the method of multiple scales. The conditions under which the oppositely traveling components of the nonlinear motion uncouple to first order are given.
Seymour, Brian R., Mortell, Michael P.
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On the Superconvergence of Galerkin Approximations to Second-Order Hyperbolic Equations

SIAM Journal on Numerical Analysis, 1980
In this note we consider semidiscrete and multistep fully discrete Galerkin approximations (in the space of smooth periodic splines $S^\mu ,\mu \geqq 2$, on a uniform mesh with mesh length h) to the solution of the initial-periodic boundary value problem for a second-order hyperbolic equation with space-varying coefficients.
Dougalis, Vassilios A., Serbin, Steven M.   +1 more
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ON A MIXED PROBLEM FOR A HYPERBOLIC EQUATION OF THE SECOND ORDER

Mathematics of the USSR-Izvestiya, 1969
Using Laplace transform methods we establish existence theorems for a classical solution of a mixed problem for various forms of hyperbolic operators of the second order.
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Carleman Estimates for Second-Order Hyperbolic Equations

Siberian Mathematical Journal, 2006
Summary: In the space of variables \((x,t)\in\mathbb R^{n+1}\), we consider a linear second-order hyperbolic equation with coefficients depending only on \(x\). Given a domain \(D\subset\mathbb R^{n+1}\) whose projection to the \(x\)-space is a compact domain \(\Omega\), we consider the question of construction of a stability estimate for a solution to
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Difference schemes for second order hyperbolic equations

International Journal for Numerical Methods in Engineering, 1976
AbstractImplicit difference methods for the wave equation in two space variables have been discussed with the help of a stability diagram. The difference methods of intermediate accuracy 0(h4+k2) have been determined. A method of order of accuracy 0(h2+k2) with minimum truncation error has also been found.
Jain, M. K., Ahuja, Raj, Bhattacharyya, S.   +2 more
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Three applications of a systematization of second order hyperbolic equations

Funkcialaj Ekvacioj, 1993
The derivation of energy estimates for initial-boundary value problems of linear second order hyperbolic equations is often very difficult and technical. To obtain such energy estimates the authors have developped in preceding papers a systematic method to reduce such problems to initial- boundary value problems for systems of first order pseudo ...
Suzuki, Fukuzo, Taniguchi, Masaru
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Circulant preconditioners for second order hyperbolic equations

BIT, 1992
The authors are concerned with the numerical solution of initial-boundary value problems for linear second order hyperbolic equations. The problems are discretized based on implicit time discretization and central differencing in the space variables with respect to uniform time and space steps.
Jin, Xiao-Qing, Chan, Raymond H.
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First-order Equations and Hyperbolic Second-order Equations

1999
The concept of a characteristic curve for a second-order equation was introduced in Chapter 1, and led to a classification of these equations. When the characteristics are real as in the hyberbolic case, they can be used to solve partial differential equations directly.
Gwynne A. Evans, Jonathan M. Blackledge, Peter D. Yardley   +2 more
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