Results 11 to 20 of about 122,957 (282)
Journal of Computational and Applied Mathematics, 1996 In this paper, we develop implicit difference schemes of O(k4 + k2h2 + h4), where k > 0, h > 0 are grid sizes in time and space coordinates, respectively, for solving the system of two space dimensional second order nonlinear hyperbolic partial ...
R. K. Mohanty, M. K. Jain, K. George
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Journal of Computational and Applied Mathematics, 2010 The authors consider a second order nonlinear hyperbolic equation. A semidiscrete finite volume element method, based on the two-grid method, is suggested and analyzed. The idea of the two grid method is to reduce the nonlinear and nonsymmetric problem on a fine grid into a linear and symmetric problem on a coarse grid.
Chuanjun Chen, W. Liu
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Superconvergence analysis of a two-grid method for nonlinear hyperbolic equations
Computers and Mathematics With Applications, 2020 In this paper, the superconvergence analysis of a second-order fully discrete scheme with two-grid method (TGM) is studied for the two-dimensional nonlinear hyperbolic equations by the bilinear finite element. The existence and uniqueness of the solution
Yifan Wei, D. Shi
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Evolution Equations and Control Theory, 2020 The paper is concerned with the Cauchy problem for second order hyperbolic evolution equations with nonlinear source in a Hilbert space, under the effect of nonlinear time-dependent damping.
Jun-Ren Luo, Ti‐Jun Xiao
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Journal of the Egyptian Mathematical Society, 2014 An efficient numerical method based on quintic nonpolynomial spline basis and high order finite difference approximations has been presented. The scheme deals with the space containing hyperbolic and polynomial functions as spline basis. With the help of
Navnit Jha, R. K. Mohanty
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Journal of Computational and Applied Mathematics, 1996 R. K. Mohanty, M. K. Jain, K. George
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Cosine methods for nonlinear second-order hyperbolic equations
Mathematics of Computation, 1989 We construct and analyze efficient, high-order accurate methods for approximating the smooth solutions of a class of nonlinear, second-order hyperbolic equations. The methods are based on Galerkin type discretizations in space and on a class of fourth-order accurate two-step schemes in time generated by rational approximations to the cosine ...
L. Bales, V. Dougalis
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Computers & Mathematics with Applications, 1986 Error estimates are proved for finite element approximations to the solution of the initial-value problem \[ u_{tt}=\sum^{n}_{j,k=1}\partial /\partial x_ j(a_{jk}(x,t,u)\partial u/\partial x_ k)-a_ 0(t,x\quad,u)u+f(x,t,u)\quad in\quad \Omega \times [0,\tau], \] \(u=0\) in \(\partial \Omega \times [0,\tau]\), \(u(0)=u^ 0\), \(u_ t(0)=u^ 0_ t\) in ...
L. Bales
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Propagation of c°° regularity for fully nonlinear second order strictly hyperbolic equations in two variables [PDF]
Transactions of the American Mathematical Society, 1985 It is shown that if u u is a C 3 {C^3} solution of a fully nonlinear second order strictly hyperbolic equation in two variables, then u u is C ∞ {C^\infty } at a point m m as soon as it is
P. Godin
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Computers & Mathematics with Applications, 1988 In an earlier paper [ibid. 12A, 581-604 (1986; Zbl 0596.65079)] the author considered the problem: \[ (1)\quad u_{tt}=\sum^{N}_{j,k=1}\partial /\partial x_ j[a_{j_ k}(x,t,u)\partial u/\partial x_ k]-a_ 0(x,t,u)u+f(x,t,u,u_ t,\nabla u) \] u\(=0\) in \(\Omega\) \(\times [0,\tau]\) \(u(0)=u^ 0\), \(u_ t(0)=u^ 0_ t\) in \(\Omega\), where \(\Omega\) is ...
L. Bales
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