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

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
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References:

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