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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:
65M70Spectral, collocation and related methods (IVP of PDE)
65M06Finite difference methods (IVP of PDE)
35L15Second order hyperbolic equations, initial value problems
65M12Stability and convergence of numerical methods (IVP of PDE)
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