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Zbl 1172.65046
Ashyralyev, Allaberen; Koksal, Mehmet Emir
On the numerical solution of hyperbolic PDEs with variable space operator. (English)
[J] Numer. Methods Partial Differ. Equations 25, No. 5, 1086-1099 (2009). ISSN 0749-159X; ISSN 1098-2426/e

Summary: Difference schemes with first- and second-order of accuracy in time and second order of accuracy in the space variables for the numerical solution of an initial-boundary value problem for a multidimensional hyperbolic equation with variable coefficients are considered. Stability estimates for the solution of these difference schemes and for the first and second order difference derivatives are obtained. Numerical methods are proposed for solving the one-dimensional hyperbolic partial differential equation.

MSC 2000:: *65M06 Finite difference methods (IVP of PDE)
65M12 Stability and convergence of numerical methods (IVP of PDE)
65M15 Error bounds (IVP of PDE)
35L15 Second order hyperbolic equations, initial value problems

Keywords: difference schemes; hyperbolic equation; Matlab implementation; numerical examples; error estimates

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