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On the numerical solution of fractional hyperbolic partial differential equations. (English) Zbl 1184.65083
Summary: A stable difference scheme for the numerical solution of a mixed problem for a multidimensional fractional hyperbolic equation is presented. Stability estimates for the solution of this difference scheme and for the first and second orders difference derivatives are obtained. A procedure of a modified Gauss elimination method is used for solving this difference scheme in the case of one-dimensional fractional hyperbolic partial differential equations.

MSC:
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35R11 Fractional partial differential equations
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
35L99 Hyperbolic equations and hyperbolic systems
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References:
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