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The Maximal Regularity of Nonlinear Second-Order Hyperbolic Boundary Differential Equations [PDF]
AxiomsIn this paper, we show the maximal regularity of nonlinear second-order hyperbolic boundary differential equations. We aim to show if the given second-order partial differential operator satisfies the specific ellipticity condition; additionally, if ...
Xingyu Liu
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An H1-Galerkin Expanded Mixed Finite Element Approximation of Second-Order Nonlinear Hyperbolic Equations [PDF]
Abstract and Applied Analysis, 2013 We investigate an H1-Galerkin expanded mixed finite element approximation of nonlinear second-order hyperbolic equations, which model a wide variety of phenomena that involve wave motion or convective transport process.
Zhaojie Zhou, Weiwei Wang, Huanzhen Chen
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Homotopy Analysis Transform Method for a Singular Nonlinear Second-Order Hyperbolic Pseudo-Differential Equation [PDF]
AxiomsIn this study, we employed the homotopy analysis transform method (HATM) to derive an iterative scheme to numerically solve a singular second-order hyperbolic pseudo-differential equation.
Said Mesloub, Hassan Eltayeb Gadain
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Discontinuous Galerkin discretization in time of systems of second-order nonlinear hyperbolic equations [PDF]
ESAIM: Mathematical Modelling and Numerical Analysis, 2021 In this paper we study the finite element approximation of systems of second- order nonlinear hyperbolic equations. The proposed numerical method combines a hp - version discontinuous Galerkin finite element approximation in the time direction with an ...
Aili Shao
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Blowups for a class of second order nonlinear hyperbolic equations: a reduced model of nonlinear Jeans instability [PDF]
Mathematische Annalen, 2022 Understanding the formation of nonlinear structures in the universe and stellar systems is crucial. The nonlinear Jeans instability plays a key role in these formation processes.
Chao Liu
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Bi-Finite Difference Method to Solve Second-Order Nonlinear Hyperbolic Telegraph Equation in Two Dimensions [PDF]
Mathematical Problems in Engineering, 2022 This study introduces a computational scheme by the bi-finite difference method (Bi-FDM) to solve the hyperbolic telegraph equation in two dimensions.
K. Raslan +3 more
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Cosine methods for nonlinear second-order hyperbolic equations [PDF]
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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Известия Иркутского государственного университета: Серия "Математика", 2021 The article considers second-order system of linear stochastic partial differential equations of hyperbolic type with Goursat boundary conditions. Earlier, in a number of papers, representations of the solution Goursat problem for linear stochastic ...
K.B. Mansimov, R.O. Mastaliyev
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Networks and Heterogeneous MediaThis paper focused on approximating a second-order nonlinear hyperbolic optimal control problem. By introducing a new variable, the hyperbolic equation was converted into two parabolic equations.
Huanhuan Li +3 more
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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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