Akademik Veri Yönetim Sistemi
Computational and Applied Mathematics, cilt.45, sa.10, 2026 (SCI-Expanded, Scopus)
This study presents a robust approach for addressing the auto-convolution Volterra integral equations (AVIEs). It handles both smooth and weakly singular kernels. The method uses a mesh-free collocation strategy with radial basis functions (RBFs). Furthermore, the method is extended to initial value problems for auto-convolution Volterra integral–differential equations (AVIDEs). The scheme combines RBFs evaluated at selected nodes with the collocation procedure to yield highly reliable numerical solutions to these equations. A significant characteristic of this method is its independence from a structured grid. This meshless aspect facilitates implementation, enhances computational efficiency, and reduces memory consumption. The numerical scheme consists of converting the AVIDEs into an equivalent class of integral equations. The equations obtained from this conversion can be re-expressed as a system of algebraic equations, thereby enabling a simple and efficient numerical solution. The effectiveness of the developed scheme is evaluated through a series of numerical experiments on various test problems. The findings align with the theoretical error predictions. Moreover, a comparative evaluation with exact solutions, the moving least squares (MLS) technique, and other well-known computational approaches highlights the high robustness and superior performance of the developed approach.