An efficient method for fractional nonlinear differential equations by quasi‐Newton's method and simplified reproducing kernel method. (17th September 2017)

• Record Type: Journal Article
• Authors: Xu, Minqiang; Niu, Jing; Lin, Yingzhen
• Is Part Of: Mathematical methods in the applied sciences. Volume 41:Number 1(2018)
• Page Start: 5
• Page End: 14
• Publication Date: 2017-09-17
• Subjects: convergence analysis -- fractional -- nonlinear -- quasi‐Newton's method -- simplified reproducing kernel method; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.4590
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : An efficient method for nonlinear fractional differential equations is proposed in this paper. This method consists of 2 steps. First, we linearize the nonlinear operator equation by quasi‐Newton's method, which is based on Fréchet derivative . Then we solve the linear fractional differential equations by the simplified reproducing kernel method. The convergence of the quasi‐Newton's method is discussed for the general nonlinear case as well. Finally, some numerical examples are presented to illustrate accuracy, efficiency, and simplicity of the method.