Improving Variational Iteration Method with Auxiliary Parameter for Nonlinear Time-Fractional Partial Differential Equations

Mehmet Giyas Sakar () and Onur Saldır ()
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Mehmet Giyas Sakar: Yuzuncu Yıl University
Onur Saldır: Yuzuncu Yıl University

Journal of Optimization Theory and Applications, 2017, vol. 174, issue 2, No 10, 530-549

Abstract: Abstract In this research, we present a new approach based on variational iteration method for solving nonlinear time-fractional partial differential equations in large domains. The convergence of the method is shown with the aid of Banach fixed point theorem. The maximum error bound is specified. The optimal value of auxiliary parameter is obtained by use of residual error function. The fractional derivatives are taken in the Caputo sense. Numerical examples that involve the time-fractional Burgers equation, the time-fractional fifth-order Korteweg–de Vries equation and the time-fractional Fornberg–Whitham equation are examined to show the appropriate properties of the method. The results reveal that a new approach is very effective and convenient.

Keywords: Variational iteration method; Auxiliary parameter; Optimization; Time-fractional partial differential equation; Caputo-type derivative; 65M99; 65K10 (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s10957-017-1127-y

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