Open AccessUsing Chebyshev Polynomials in Solving Diffusion Equations
Author(s) -
Ghuson Saeid Abed
Publication year - 2021
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1879/2/022095
Subject(s) - chebyshev polynomials , mathematics , chebyshev equation , differential equation , diffusion equation , partial differential equation , dimension (graph theory) , mathematical analysis , chebyshev nodes , variable (mathematics) , diffusion , first order partial differential equation , convergence (economics) , classical orthogonal polynomials , chebyshev filter , stability (learning theory) , orthogonal polynomials , pure mathematics , computer science , physics , economy , machine learning , economic growth , economics , thermodynamics , service (business)
In this work, we modified Chebyshev polynomials of the first kind to match the characteristics of a second order differential equation that is a result of a separation of the variable technique used to solve a partial differential diffusion equation. The resultant polynomials solution in one spatial dimension is found and the corresponding changing parameters for the first order differential equation in time are extracted accordingly. The method is tested for applicability, stability, and convergence.