An Effective Numerical Approach for Solving Second-Kind Fredholm Integral Equations

In this paper, a numerical approach to solving second-kind Fredholm integral equations using shifted Chebyshev polynomials is presented. In order to approximate the solution and convert the integral equation into a system of algebraic equations, we use shifted Chebyshev polynomials as basis functions. The shifted Chebyshev polynomials provide superior approximation qualities that increase accuracy and convergence rates. Numerical experiments show that the suggested approach is successful in solving several classes of Fredholm integral equations, and its stability and efficiency are examined. The outcomes demonstrate the method's advantages over conventional numerical techniques