## 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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