Akademik Veri Yönetim Sistemi
Journal of Computational and Applied Mathematics, cilt.480, 2026 (SCI-Expanded, Scopus)
In this study, a novel approach is proposed to approximate the solution of second order Fredholm integro-differential equations. The proposed method extends the residual method used for solving ordinary differential equations. This method is based on approximating the solution of initial value problems using a Bézier curve. For the extension of the method, some novel formulas are derived to obtain the integral of the product of Bernstein basis functions and analytic functions. The proposed method is also applied to boundary value problems with minor modifications. The most significant feature of the proposed method is its ease of application to various problems, due to its simplicity and flexibility. Error analysis is provided for both initial and boundary value problems, demonstrating that this method achieves a high order of accuracy. In order to demonstrate the accuracy and efficiency of the method, several numerical examples are provided, and their results are compared with those obtained by other methods in the literature. The findings indicate that the proposed method is highly effective and can serve as a viable alternative to existing techniques for solving Fredholm integro-differential equations.