عنوان	Piecewise Hermite-type Collocation Tecniques for Numerical Solution of Second-kind Volterra Integral Equations with Weakly Singular Highly Oscillatory Fourier Kernels
نوع پژوهش	پایان نامه
کلیدواژه‌ها	Volterra integral equation, Weakly singular kernel, Highly oscillatory kernel, Hermite collocation method, Spectral approximation, Convergence analysis.
چکیده	In this thesis, the piecewise Hermite-type collocation method is presented for solving second-kind Volterra integral equations with weakly singular highly oscillatory Fourier kernels. These equations pose significant challenges for classical numerical techniques due to the combination of weak singularities and rapid oscillations, which often lead to a loss of accuracy. The proposed approach employs Hermite interpolation, utilizing both function values and derivatives at the initial point to enhance the convergence order and stability of the solution. Oscillatory moments are computed efficiently using Kummer hypergeometric and Beta functions. Theoretical analysis establishes the existence and uniqueness of solutions and derives error bounds demonstrating that accuracy improves as the oscillatory frequency increases. Furthermore, the performance of the proposed method is compared with the hybridization of block-pulse and Taylor polynomials method. Numerical experiments validate the theoretical findings, showing that the Hermite-type collocation techniques yield superior accuracy and efficiency compared to the block-pulse functions method and other existing collocation methods, particularly in high-frequency regimes.
پژوهشگران	روشنک لطفی کار (استاد راهنما)، محمد خلف سالم (دانشجو)