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NUMERICAL SOLUTION OF LINEAR FREEHOLD INTEGRAL EQUATION OF BY USING NEWTON-COTES QUADRATURE METHOD
(Wolkite University, 2023-06-20) SHEGA GASHAW
In this thesis, we discussed the numerical solution of the linear Fredholm integral equation by using the Newton-cotes quadrature rule and the Lagrange interpolation method. Lin ear Fredholm integral equation which can not be easily evaluated analytically. This thesis was concerned with the numerical method. Newton-cotes quadrature method was used to transform the linear Fredholm integral equation into a system algebraic equation. It shows that the approximate solution is uniformly convergent to the exact solution. In addition to demonstrating the efficiency and applicability of the proposed method, several numerical examples are included which confirm the convergent results. After introducing the type of integral equation we were investigate some numerical methods for solving the Freehold in tegral equation of the second kind. For the numerical treatment of the Freehold integral equation, we implemented the following numerical method; the Quadrature method and the Trapezoidal rule. The mathematical framework of these numerical method with their convergence properties was presented. These numerical method will be illustrated by some numerical examples. Comparisons between these method was drawn.