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On solving partial differential equations of fractional order by using the variational iteration method and multivariate Padé approximations. (English) Zbl 1413.65401
Summary: In this article, multivariate Padé approximation and variational iteration method proposed by He is adopted for solving linear and nonlinear fractional partial differential equations. The fractional derivatives are described in the Caputo sense. Numerical illustrations that include nonlinear time-fractional hyperbolic equation and linear fractional Klein-Gordon equation are investigated to show efficiency of multivariate Padé approximation. Comparison of the results obtained by the variational iteration method with those obtained by multivariate Padé approximation reveals that the present methods are very effective and convenient.

MSC:
65M99 Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems
41A21 Padé approximation
35R11 Fractional partial differential equations
35L70 Second-order nonlinear hyperbolic equations
35Q53 KdV equations (Korteweg-de Vries equations)
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