Solving singular integral equations by using orthogonal polynomials

A Direct Method for Numerically Solving Integral Equations System Using Orthogonal Triangular Functions

Solving a class of nonlinear two-dimensional Volterra integral equations by using two-dimensional triangular orthogonal functions

In this paper, the two-dimensional triangular orthogonal functions (2D-TFs) are applied for solving a class of nonlinear two-dimensional Volterra integral equations. 2D-TFs method transforms these integral equations into a system of linear algebraic equations. The high accuracy of this method is verified through a numerical example and comparison of the results with the other numerical methods.

Fractional Calculus for Solving Abel’s Integral Equations Using Chebyshev Polynomials

Abstract In this paper, the numerical method for solving Abel’s integral equations is presented. This method is based on fractional calculus. Also, Chebyshev polynomials are utilized to apply fractional properties for solving Abel’s integral equations of the first and second kind. The fractional operator is considered in the sense of RiemannLiouville. Although Abel’s integral equations as singu...

New Stable Numerical Solutions of Singular Integral Equations of Abel Type by Using Normalized Bernstein Polynomials

A new numerical method, based on the normalized Bernstein polynomials for solving singular integral equations of Abel type is presented here in this paper. We construct an othonormal family { } i n i b 0 = of polynomials of degree n from the th n degree Bernstein polynomials n i B and use them as a basis to approximate the known and unknown functions ) (x f and ) (x φ respectively in the Abel’s...

a direct method for numerically solving integral equations system using orthogonal triangular functions

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A spectral method based on Hahn polynomials for solving weakly singular fractional order integro-differential equations

In this paper, we consider the discrete Hahn polynomials and investigate their application for numerical solutions of the fractional order integro-differential equations with weakly singular kernel .This paper presented the operational matrix of the fractional integration of Hahn polynomials for the first time. The main advantage of approximating a continuous function by Hahn polynomials is tha...