A new fourth-order compact finite difference scheme for the two-dimensional second-order hyperbolic equation. (English) Zbl 1168.65373

Ding, Hengfei; Zhang, Yuxin

J. Comput. Appl. Math. 230, No. 2, 626-632 (2009).

Summary: We propose a three level compact difference scheme of \(O(\tau^4+h^4)\) for the difference solution of a two-dimensional second order non-homogeneous linear hyperbolic equation
\[ u_{tt}+2\alpha u_t+\beta^2 u=u_{xx}+u_{yy}+f(x,y,t),\quad 0<x,y<1, \;t>0, \]
where \(\alpha >\beta \geq 0\). Stability analysis of the method has been carried out. Finally, numerical examples are used to illustrate the efficiency of the new difference scheme.

MSC:

65M06	Finite difference methods for initial value and initial-boundary value problems involving PDEs
65M12	Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
65M15	Error bounds for initial value and initial-boundary value problems involving PDEs
35L15	Initial value problems for second-order hyperbolic equations

Keywords:

linear hyperbolic equation; high accuracy; stability; compact difference scheme; error estimates; numerical examples

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