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

✍ Scribed by M.M. Chawla; M.A. Al-Zanaidi

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 817 KB
• Volume: 33
• Category: Article
• ISSN: 0895-7177
• DOI: 10.1016/s0895-7177(00)00253-3

✦ Synopsis

present a class of eztendcd one-step time integration schemes for the integration of second-order nonlinear hyperbolic equations utt = c% 25 + p(z, 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.