TY - EJOU
AU - Reutskiy, Sergiy
AU - Zhang, Yuhui
AU - Lu, Jun
AU - Pubu, Ciren
TI - A Novel Method for Linear Systems of Fractional Ordinary Differential Equations with Applications to Time-Fractional PDEs
T2 - Computer Modeling in Engineering \& Sciences
PY - 2024
VL - 139
IS - 2
SN - 1526-1506
AB - 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 form of 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.
KW - System of FODEs; numerical solution; Müntz polynomial basis; time fractional PDE; BSM collocation method
DO - 10.32604/cmes.2023.044878