Fractional Chebyshev collocation method

The fractional Chebyshev collocation (FCC) method is an efficient spectral method for solving a system of linear fractional-order differential equations (FDEs) with discrete delays. ^[1]

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Table of Contents

1. 8 relations: Chebyshev polynomials, Collocation method, Differential equation, Discretization, Finite difference method, Fractional calculus, Linear map, Spectral method.

Chebyshev polynomials

The Chebyshev polynomials are two sequences of polynomials related to the cosine and sine functions, notated as T_n(x) and U_n(x).

See Fractional Chebyshev collocation method and Chebyshev polynomials

Collocation method

In mathematics, a collocation method is a method for the numerical solution of ordinary differential equations, partial differential equations and integral equations.

See Fractional Chebyshev collocation method and Collocation method

Differential equation

In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives.

See Fractional Chebyshev collocation method and Differential equation

Discretization

In applied mathematics, discretization is the process of transferring continuous functions, models, variables, and equations into discrete counterparts.

See Fractional Chebyshev collocation method and Discretization

Finite difference method

In numerical analysis, finite-difference methods (FDM) are a class of numerical techniques for solving differential equations by approximating derivatives with finite differences.

See Fractional Chebyshev collocation method and Finite difference method

Fractional calculus

Fractional calculus is a branch of mathematical analysis that studies the several different possibilities of defining real number powers or complex number powers of the differentiation operator D D f(x).

See Fractional Chebyshev collocation method and Fractional calculus

Linear map

In mathematics, and more specifically in linear algebra, a linear map (also called a linear mapping, linear transformation, vector space homomorphism, or in some contexts linear function) is a mapping V \to W between two vector spaces that preserves the operations of vector addition and scalar multiplication.

See Fractional Chebyshev collocation method and Linear map

Spectral method

Spectral methods are a class of techniques used in applied mathematics and scientific computing to numerically solve certain differential equations.

See Fractional Chebyshev collocation method and Spectral method

References

[1] https://en.wikipedia.org/wiki/Fractional_Chebyshev_collocation_method

Also known as Fractional Chebyshev Collocation (FCC) Method.

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