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High order implicit collocation method for the solution of two-dimensional linear hyperbolic equation. (English) Zbl 1156.65087

Summary: We introduce a high-order accurate method for solving a two dimensional linear hyperbolic equation. We apply a compact finite difference approximation of fourth order for discretizing the spatial derivatives of the linear hyperbolic equation and a collocation method for the time component. The resulted method is unconditionally stable and solves the two-dimensional linear hyperbolic equation with high accuracy. In this technique, the solution is approximated by a polynomial at each grid point the coefficients of which are determined by solving a system of linear equations. Numerical results show that the compact finite difference approximation of fourth order and the collocation method give a very efficient approach for solving the two dimensional linear hyperbolic equation.

MSC:

65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35L15 Initial value problems for second-order hyperbolic equations
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
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References:

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