Author:
Asl Mohammad Shahbazi,Javidi Mohammad,Yan Yubin
Abstract
AbstractIn this paper, two novel high order numerical algorithms are proposed for solving fractional differential equations where the fractional derivative is considered in the Caputo sense. The total domain is discretized into a set of small subdomains and then the unknown functions are approximated using the piecewise Lagrange interpolation polynomial of degree three and degree four. The detailed error analysis is presented, and it is analytically proven that the proposed algorithms are of orders 4 and 5. The stability of the algorithms is rigorously established and the stability region is also achieved. Numerical examples are provided to check the theoretical results and illustrate the efficiency and applicability of the novel algorithms.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Algebra and Number Theory,Analysis
Reference47 articles.
1. Simpson, R., Jaques, A., Nuñez, H., Ramirez, C., Almonacid, A.: Fractional calculus as a mathematical tool to improve the modeling of mass transfer phenomena in food processing. Food Eng. Rev. 5(1), 45–55 (2013)
2. Gepreel, K.A., Nofal, T.A.: Optimal homotopy analysis method for nonlinear partial fractional differential equations. Math. Sci. 9(1), 47–55 (2015)
3. Herzallah, M.A., Gepreel, K.A.: Approximate solution to the time–space fractional cubic nonlinear Schrodinger equation. Appl. Math. Model. 36(11), 5678–5685 (2012)
4. Gepreel, K.A., Nofal, T.A., Alotaibi, F.M.: Numerical solutions for the time and space fractional nonlinear partial differential equations. J. Appl. Math. 2013, Article ID 482419 (2013)
5. Roohi, M., Aghababa, M.P., Haghighi, A.R.: Switching adaptive controllers to control fractional-order complex systems with unknown structure and input nonlinearities. Complexity 21(2), 211–223 (2015)
Cited by
11 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献