Comparison Between the Numerical Methods in Solving the Volterra and Fredholm Non-Linear Integral Equations of the Second Kind
Keywords:
Volterra equation, Fredholm, Abel's problem, Laplace transforms, gamma function, Simpson’s Method, Trapezoidal MethodAbstract
In this paper, a simple comparison is made between some numerical methods for solving integral equations and an analytical method. Methods such as the Simpson and trapezoidal methods, along with other numerical approaches, are explored for solving Fredholm, Volterra, and Abel integral equations. The effectiveness of these methods in finding convergent results is explained. Comparing different numerical techniques to solve nonlinear integral equations of Fredholm and Volterra, which are second-kind equations, is the goal of this thesis. Additionally, it provides a brief study of numerical methods in solving and comparing these equations due to their importance in various scientific, engineering, and physics applications. These methods prove to be more effective in many applications. The thesis is presented in three main chapters.
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