Comparison of the Results of the Approximate Solution of Linear Fredholm Integral Equations of the Second Kind by Various Methods
Keywords:
linear integral equation, optimal quadrature formula, quadrature formula with derivatives, system of algebraic equations, maximum absolute errorAbstract
The approximate solution of linear Fredholm integral equations of the second kind is one of the pressing problems in the field of computational mathematics today. Most researchers offer various approximate methods for solving integral equations. This work is devoted to comparing various approximate methods for solving linear Fredholm equations of the second kind. The main goal of the work is to determine the most effective method. Our method is the use of optimal quadrature formulas with derivatives to solve linear Fredholm integral equations of the second kind. The effectiveness of the method depends on the accuracy of the results. In this case, the exact solution was used to compare the results. The effectiveness of this method is proven.
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