Mathematics

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Numerical Methods for Solving Volterra-Fredholm Integral Equation of the Second Kind
(Ruba Nasser Ali Salman, 2019-01-08) Salman, Ruba
In this thesis we focus on the numerical handling of the Volterra-Fredholm integral equation of the second kind due to their wide range of physical applications such as theory of elasticity, airfoil theory, elastic constant problems and molecular conduction. After the classification of integral equations, we will investigate some numerical methods for solving the Volterra-Fredholm integral equation of the second kind. These include: Taylor collocation method, least squares approximation method, Legendre collocation method and Lagrange interpolation method. The mathematical framework of these numerical methods together with their convergence properties will be analyzed. Some numerical examples implementing these numerical methods have been illustrated. Numerical results clearly show that the Lagrange interpolation method is one of the most powerful and efficient numerical methods for solving Volterra-Fredholm integral equation of the second kind in comparison with the other numerical methods used in this thesis. On the other hand, the Taylor collocation method is one of the fastest methods in terms of CPU-time for solving Volterra-Fredholm integral equation of the second kind.