Numerical Solutions of Duffing Equations Involving Linear Integral with Shifted Chebyshev Polynomials

Legendre polynomials for numerical solution of linear fuzzy Fredholm integral equations

Numerical Solutions of Fredholm Integral Equations Using Bernstein Polynomials

In this paper, Bernstein piecewise polynomials are used to solve the integral equations numerically. A matrix formulation is given for a non-singular linear Fredholm Integral Equation by the technique of Galerkin method. In the Galerkin method, the Bernstein polynomials are exploited as the linear combination in the approximations as basis functions. Examples are considered to verify the effect...

Application of Chebyshev Polynomials for Solving Abel's Integral Equations of the First and Second Kind

In this paper, a numerical implementation of an expansion method is developed for solving Abel's integral equations of the first and second kind. The solution of such equations may demonstrate a singular behaviour in the neighbourhood of the initial point of the interval ofintegration. The suggested method is based on the use of Taylor series expansion to overcome the singularity which le...

Chebyshev polynomials for solving two dimensional linear and nonlinear integral equations of the second kind

In this paper, an efficient method is presented for solving two dimensional Fredholm and Volterra integral equations of the second kind. Chebyshev polynomials are applied to approximate a solution for these integral equations. This method transforms the integral equation to algebraic equations with unknown Chebyshev coefficients. The high accuracy of this method is verified through some numeric...

Numerical Solutions of Monic Chebyshev Polynomials on Large Scale Differentiation

In this paper, a new formula of the spectral differentiation matrices is presented. Therefore, the numerical solutions for higher-order differential equations are presented by expanding the unknown solution in terms of monic Chebyshev polynomials. The resulting systems of linear equations are solved directly for the values of the solution at the extreme points of the Chebyshev polynomial of ord...