On the Numerical Solution of Volterra-Fredholm Integral Equations with Exponential Kernal using Chebyshev and Legendre Collocation Methods (original) (raw)

Legendre and Chebyshev collocation methods are presented to solve numerically the Voltterra-Fredholm integral equations with the exponential kernel. We transform the Volterra Fredholm integral equations to a system of Fredholm integral equations of the second kind,a system Fredholm integral equation with the exponential kernel is obtained and will be solved using Legendre and Chebyshev polynomials. This leads to a system of algebraic equations with Legendre or Chebychev coefficients. Thus, by solving the matrix equation, Legendre and Chebychev coefficients are obtained.A numerical example is included to certify the validity and applicability of the proposed technique.