A class of one-step time integration schemes for second-order hyperbolic differential equations

We present a class of extended one-step time integration schemes for the integration of second-order nonlinear hyperbolic equations u tt = c 2 u xx + p( x,t,u), subject to initial conditions and boundary conditions of Dirichlet type or of Neumann type. We obtain one-step time integration schemes of...

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Bibliographic Details
Published in:Mathematical and computer modelling 2001-02, Vol.33 (4), p.431-443
Main Authors: Chawla, M.M., Al-Zanaidi, M.A.
Format: Article
Language:English
Subjects:
Exact sciences and technology
Extended one-step time integration schemes
Extended trapezoidal formula
Mathematical analysis
Mathematics
Modified Simpson rule
Newmark method
P-stability
Partial differential equations
Sciences and techniques of general use
Second-order nonlinear hyperbolic equations
Sine-Gordon equation
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Summary:We present a class of extended one-step time integration schemes for the integration of second-order nonlinear hyperbolic equations u tt = c 2 u xx + p( x,t,u), subject to initial conditions and boundary conditions of Dirichlet type or of Neumann type. We obtain one-step time integration schemes of orders two, three, and four; the schemes are unconditionally stable. For nonlinear problems, the second- and the third-order schemes have tridiagonal Jacobians, and the fourth-order schemes have pentadiagonal Jacobians. The accuracy and stability of the obtained schemes is illustrated computationally by considering numerical examples, including the sine-Gordon equation.
ISSN:0895-7177
1872-9479
DOI:10.1016/S0895-7177(00)00253-3