Chebyshev, first problem - Open Access .click

Journal of Physical Sciences, 2019
Purpose: The purpose of this study is to derive a numerical solver for first order initial value problems of ordinary differential equation via the combination of Chebyshev polynomial and exponential function.Methodology: A new numerical method for solving Initial Value Problems of first order ordinary differential equation is developed.
R. B. Ogunrinde +3 more
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Sobolev Orthogonal Polynomials Associated with Chebyshev Polynomials of the First Kind and the Cauchy Problem for Ordinary Differential Equations

Differential Equations, 2018
This paper deals with polynomials $T_{r,n}(x)$ generated by Chebyshev polynomials $T_n(x)$ and forming a Sobolev orthonormal system with an inner product. The paper establishes that the Fourier sums of the mentioned polynomials give an efficient tool for solving the Cauchy problem for ordinary differential equations approximately.
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The Approximate Solution for Multi-term the Fractional Order Initial Value Problem Using Collocation Method Based on Shifted Chebyshev Polynomials of the First Kind

2018
Nowadays, to survive and promote the market competition, multi-item business strategy is more effective for any production/manufacturing sector. Many physical problems can be best model by using fractional differential equation (FDE). In this paper, we propose the approximate scheme to solve multi-term fractional order initial value problem.
Vijay Saw, Sushil Kumar 0002
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chebyshev polynomials
physics
operational matrix