Numerical Multistep Approach for Solving Fractional Partial Differential Equations

被引:93
作者
Al-Smadi, Mohammed [1 ]
Freihat, Asad [1 ]
Khalil, Hammad [2 ]
Momani, Shaher [3 ,4 ]
Khan, Rahmat Ali [1 ]
机构
[1] Al Balqa Appl Univ, Ajloun Coll, Dept Appl Sci, Ajloun 26816, Jordan
[2] Univ Malakand, Dept Math, Kpk, Pakistan
[3] Univ Jordan, Fac Sci, Dept Math, Amman 11942, Jordan
[4] King Abdulaziz Univ, Nonlinear Anal & Appl Math NAAM Res Grp, Fac Sci, Jeddah 21589, Saudi Arabia
关键词
Partial differential equations; time fractional heat equations; multistep schemes; GENERALIZED TAYLORS FORMULA; BOUNDARY-VALUE-PROBLEMS; TRANSFORM METHOD; SYSTEMS; ORDER;
D O I
10.1142/S0219876217500293
中图分类号
T [工业技术];
学科分类号
08 ;
摘要
In this paper, we proposed a novel analytical technique for one-dimensional fractional heat equations with time fractional derivatives subjected to the appropriate initial condition. This new analytical technique, namely multistep reduced differential transformation method (MRDTM), is a simple amendment of the reduced differential transformation method, in which it is treated as an algorithm in a sequence of small intervals, in order to hold out accurate approximate solutions over a longer time frame compared to the traditional RDTM. The fractional derivatives are described in the Caputo sense, while the behavior of solutions for different values of fractional order a compared with exact solutions is shown graphically. The analysis is accompanied by four test examples to demonstrate that the proposed approach is reliable, fully compatible with the complexity of these equations, and can be strongly employed for many other nonlinear problems in fractional calculus.
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页数:15
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