Premium
An improved numerical technique for distributed‐order time‐fractional diffusion equations
Author(s) -
Dehestani Haniye,
Ordokhani Yadollah,
Razzaghi Mohsen
Publication year - 2021
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.22731
Subject(s) - mathematics , algebraic equation , gaussian quadrature , legendre polynomials , collocation method , quadrature (astronomy) , collocation (remote sensing) , matrix (chemical analysis) , integral equation , nyström method , mathematical analysis , computer science , differential equation , nonlinear system , ordinary differential equation , physics , materials science , engineering , quantum mechanics , machine learning , electrical engineering , composite material
This paper considers a novel numerical method based on Lucas‐fractional Lucas functions (L‐FL‐Fs) and collocation method for solving the distributed‐order time‐fractional diffusion equations. In the current investigation, we express the new computational process to gain the integral operational matrix for Lucas polynomials (LPs) and fractional Lucas functions (FLFs). The proposed method creates operational matrices with high accuracy that affect to accuracy and efficiency of the computational scheme directly. The operational matrices, by combining Legendre–Gauss quadrature rule and collocation method, reduce the given distributed‐order time‐fractional diffusion equation to a system of algebraic equations. Also, we investigate the error estimation associated with the presented idea. At last, several examples are given to demonstrate the accuracy and easy implementation of the proposed method.