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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:
65M06Finite difference methods (IVP of PDE)
35R11Fractional partial differential equations
65M12Stability and convergence of numerical methods (IVP of PDE)
35L99Hyperbolic equations and systems