A Novel Method for Linear Systems of Fractional Ordinary Differential Equations with Applications to Time-Fractional PDEs  

作　　者：Sergiy Reutskiy Yuhui Zhang Jun Lu Ciren Pubu 

机构地区：[1]A.Pidhornyi Institute of Mechanical Engineering Problems of NAS of Ukraine,Kharkiv,61046,Ukraine [2]College of Mechanics and Materials,Hohai University,Nanjing,211100,China [3]Nanjing Hydraulic Research Institute,Nanjing,210029,China [4]Shigatse Everest Urban Investment and Development Group Co,Ltd.,857000,China

出　　处：《Computer Modeling in Engineering & Sciences》2024年第5期1583-1612,共30页工程与科学中的计算机建模（英文）

基　　金：funded by the National Key Research and Development Program of China(No.2021YFB2600704);the National Natural Science Foundation of China(No.52171272);the Significant Science and Technology Project of the Ministry of Water Resources of China(No.SKS-2022112).

摘　　要：This paper presents an efficient numerical technique for solving multi-term linear systems of fractional ordinary differential equations(FODEs)which have been widely used in modeling various phenomena in engineering and science.An approximate solution of the system is sought in the formof the finite series over the Müntz polynomials.By using the collocation procedure in the time interval,one gets the linear algebraic system for the coefficient of the expansion which can be easily solved numerically by a standard procedure.This technique also serves as the basis for solving the time-fractional partial differential equations(PDEs).The modified radial basis functions are used for spatial approximation of the solution.The collocation in the solution domain transforms the equation into a system of fractional ordinary differential equations similar to the one mentioned above.Several examples have verified the performance of the proposed novel technique with high accuracy and efficiency.

关 键 词：System of FODEs numerical solution Müntz polynomial basis time fractional PDE BSM collocation method 

分 类 号：O175[理学—数学]