Finite Difference and Iteration Methods for Fractional Hyperbolic Partial Differential Equations with the Neumann Condition

摘要

The numerical and analytic solutions of the mixedproblem for multidimensional fractional hyperbolic partialdifferential equations with the Neumann condition are presented. Thestable difference scheme for the numerical solution of the mixedproblem for the multidimensional fractional hyperbolic equation withthe Neumann condition is presented. Stability estimates for thesolution of this difference scheme and for the first- and second-order difference derivatives are obtained. A procedure of modifiedGauss elimination method is used for solving this difference schemein the case of one-dimensional fractional hyperbolic partialdifferential equations. He's variational iteration method isapplied. The comparison of these methods is presented.