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

Sakar, Mehmet; Saldır, Onur

doi:10.1007/s10957-017-1127-y

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

Atıf İçin Kopyala

Sakar M. G., Saldır O.

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, cilt.174, sa.2, ss.530-549, 2017 (SCI-Expanded)

Yayın Türü: Makale / Tam Makale
Cilt numarası: 174 Sayı: 2
Basım Tarihi: 2017
Doi Numarası: 10.1007/s10957-017-1127-y
Dergi Adı: JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
Sayfa Sayıları: ss.530-549
Van Yüzüncü Yıl Üniversitesi Adresli: Evet

Özet

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.