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A modified Chebyshev ϑ ‐weighted Crank–Nicolson method for analyzing fractional sub‐diffusion equations
Author(s) -
Erfanifar Raziyeh,
Sayevand Khosro,
Ghanbari Nasim,
Esmaeili Hamid
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.22543
Subject(s) - mathematics , discretization , convergence (economics) , chebyshev filter , algebraic equation , stability (learning theory) , relaxation (psychology) , diffusion , consistency (knowledge bases) , chebyshev iteration , chebyshev polynomials , fractional calculus , mathematical analysis , nonlinear system , computer science , discrete mathematics , physics , quantum mechanics , machine learning , economics , thermodynamics , economic growth , psychology , social psychology
This study presents a robust modification of Chebyshev ϑ ‐weighted Crank–Nicolson method for analyzing the sub‐diffusion equations in the Caputo fractional sense. In order to solve the problem, by discretization of the sub‐fractional diffusion equations using Taylor's expansion a linear system of algebraic equations that can be analyzed by numerical methods is presented. Furthermore, consistency, convergence, and stability analysis of the suggested method are discussed. In this framework, compact structures of sub‐diffusion equations are considered as prototype examples. The main advantage of the proposed method is that, it is more efficient in terms of CPU time, computational cost and accuracy in comparing with the existing ones in open literature.