Results 221 to 230 of about 8,120 (265)

Least-squares Galerkin procedure for second-order hyperbolic equations

Journal of Systems Science and Complexity, 2010
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Hui Guo, Hongxing Rui, Chao Lin
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On a method of characteristics for solving a hyperbolic equation of second order

Computing, 1978
The hyperbolic initial-boundary value problem for the second order equationa(t,x,u)utt+2b(t,x,u)utx+c(t,x,u)uxx=d(t,x,u,ut,ux) is solved by a special method of characteristics involving no difference equations forut andux. The discrete solution has an asymptotic expansion in even powers of the step size. Therefore, the numerical results can be improved
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On a class of second order Fuchsian hyperbolic equations

Annali di Matematica Pura ed Applicata, 1986
Let P be of the form: \[ (1)\quad P=-tD^ 2_ t+A(t,x,D_ y)+a(t,x)D_ t+b(t,x)D_ y+c(t,x), \] where: (i) the principal part of P; \(-tD\) \(2_ t+A(t,x,D_ y)\) is strictly hyperbolic for \(t>0.\) (ii) A(t,x,\(\cdot)\), b(t,x) and \(c(t,x)\in C^{\infty}(R_ t\times M)\), where M is a \(C^{\infty}\)-manifold without boundary. The aim of this paper is to solve
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Supplement to Cosine Methods for Nonlinear Second-Order Hyperbolic Equations

Mathematics of Computation, 1989
This is the supplement to the authors' paper [ibid. 52, No.186, 299-319 (1989; reviewed above)] providing the detailed proofs of the results on consistency, error estimates, convergence and starting schemes. Some remarks on the validity of certain hypotheses are also given in an appendix.
Bales, Laurence A., Dougalis, Vassilios A.   +1 more
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Theory of degenerate second order hyperbolic equations

Siberian Mathematical Journal, 1990
The equation mentioned in the title is: \[ Lu=\nu^ 2(t)u_{tt}- \sum^{n}_{i,j=1}\partial /\partial x_ i(a_{ij}(x,t)u_{x_ j})+au_ t+\sum^{n}_{i=1}b_ iu_{x_ i}+cu=f, \] with \(a_{ij}=a_{ji}\), \(\sum^{n}_{i,j=1}a_{ij}\xi_ i\xi_ j\geq 0\), for any \(\xi \in {\mathbb{R}}^ n\). \(\nu\) (t) is continuous on [0,1] and differentiable on (0,1].
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On a Certain Class of Hyperbolic Equations with Second-Order Integrals

Journal of Mathematical Sciences, 2020
In this paper, we examine a special class of nonlinear hyperbolic equations possessing a second-order y-integral. We clarify the structure of x-integrals and prove that they are x-integrals of a hyperbolic equation with a first-order y-integral. We also prove that this class contains the well-known Laine equation.
A. V. Zhiber, A. M. Yur’eva
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Difference scheme of second-order of accuracy on the minimal pattern for hyperbolic equations

USSR Computational Mathematics and Mathematical Physics, 1983
Translation from Zh. Vychisl. Mat. Mat. Fiz. 23, No.1, 119-126 (Russian) (1983; Zbl 0534.65049).
Belotserkovskij, O. M., Grudnitskij, V. G., Prokhorchuk, Yu. A.   +2 more
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Uniqueness In Boundary Value Problems For The Second Order Hyperbolic Equation

Canadian Journal of Mathematics, 1956
Introduction. We study linear normal hyperbolic partial differential equations of the second order, with one dependent variable u, and N independent variables xi (i = 1, … , N). The uniqueness theorem connected with the Cauchy problem for this type of equation is well known and in effect states that if u and its first normal derivatives vanish on a ...
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A note on the second order of accuracy difference schemes for hyperbolic–parabolic equations

Applied Mathematics and Computation, 2005
The nonlocal boundary value problem for hyperbolic-parabolic equations \[ \begin{cases} \frac{{d^2 u(t)}}{{dt^2}} + Au(t) = f(t), & {0 \leq t \leq 1}, \\ \frac{{du(t)}}{{dt}} + Au(t) = g(t), & {- 1 \leq t \leq 0}, \\ u({-1}) = \alpha u(\mu) + \varphi , & 0 \leq \alpha \leq 1,\;\;0 \leq \mu \leq 1.
Allaberen Ashyralyev, H. A. Yurtsever
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Second-order equations: hyperbolic equations for functions of two independent variables

1978
We start with the general quasi-linear second-order equation for a function u(x,y): $$ a{u_{xx}} + 2b{u_{xy}} + c{u_{yy}} = d, $$ (1.1) where a,b,c,d depend on x,y,u,u x ,u y . Here the Cauchy problem consists of finding a solution u of (1.1) with given (compatible) values of u,u x ,u y on a curve γ in the xy-plane.
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