Orthogonal polynomials

Work (physics)

Collocation method

Classical orthogonal polynomials

Volterra integral equation

Mathematics

Collocation (remote sensing)

Matrix (chemical analysis)

Chebyshev polynomials

Machine learning

Engineering

Mathematical analysis

Chebyshev equation

Composite material

Chebyshev nodes

Chebyshev filter

Integral equation

Materials science

Chebyshev iteration

Computer science

Differential equation

Applied mathematics

Ordinary differential equation

Mechanical engineering

Fredholm integral equation

Arabian Journal of Mathematics

This work reports a collocation algorithm for the numerical solution of a Volterra–Fredholm integral equation (V-FIE), using shifted Chebyshev collocation (SCC) method. Some properties of the shifted Chebyshev polynomials are presented. These properties together with the shifted Gauss–Chebyshev nodes were then used to reduce the Volterra–Fredholm integral equation to the solution of a matrix equation. Nextly, the error analysis of the proposed method is presented. We compared the results of this algorithm with others and showed the accuracy and potential applicability of the given method.

Chebyshev collocation treatment of Volterra–Fredholm integral equation with error analysis