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2009•Mathematical Problems in EngineeringOpen access

On the Numerical Solution of Fractional Hyperbolic Partial Differential Equations

Allaberen Ashyralyev, Fadime Dal, Zehra Pınar

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Abstract

The stable difference scheme for the numerical solution of the mixed problem for the 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 modified Gauss elimination method is used for solving this difference scheme in the case of one‐dimensional fractional hyperbolic partial differential equations.

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The stable difference scheme for the numerical solution of the mixed problem for the 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 modified Gauss elimination method is used for solving this difference scheme in the case of one‐dimensional fractional hyperbolic partial differential equations.

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Available abstract

The stable difference scheme for the numerical solution of the mixed problem for the 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 modified Gauss elimination method is used for solving this difference scheme in the case of one‐dimensional fractional hyperbolic partial differential equations.

Key concepts: Mathematics, Hyperbolic partial differential equation, FTCS scheme, Partial differential equation, Mathematical analysis, Stability (learning theory), Scheme (mathematics), Applied mathematics

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