应我校数理学院邀请，Samad Noeiaghdam 教授来我校进行学术交流，并做学术报告。

       题目：Dynamical Control on Numerical Methods for Solving Integral Equations: CESTAC Method and CADNA Library

       时间：2025年 12月 25日（星期四 ）下午14:00 –16:00

       地点：科研楼213室

     报告人简介：Dr. Samad Noeiaghdam, Research Professor of Henan Academy of Sciences, Zhengzhou, China and at the same time he is Professor of Irkutsk National Research Technical University, Russia and Faculty Member at Saveetha School of Engineering, India. His main research interests are numerical analysis, numerical methods for integral equations, ODEs and PDEs, fuzzy problems with applications, load leveling in energy storage, supply and demand systems, MHD and heat and mass transfer problems. He has more than 200 publications including several high-quality papers in top journals as well as books, chapters and conference papers. Because of his high-level activities in research and contribution to mathematical advancement globally he has been acknowledged as one of the top 2% scientists by Stanford University.

      讲座内容：The primary objective of this discussion is to present the CESTAC (Contr？le et Estimation Stochastique des Arrondis de Calculs) method together with the CADNA (Control of Accuracy and Debugging for Numerical Applications) library as effective tools for controlling error propagation and determining optimal step sizes in numerical computations. The CESTAC–CADNA framework is grounded in stochastic arithmetic, and therefore numerical schemes such as the Collocation Method, Homotopy Analysis Method (HAM), and Homotopy Perturbation Method (HPM) are implemented using stochastic arithmetic rather than conventional floating-point arithmetic. Particular emphasis is placed on the application of these approaches to the numerical solution of various classes of Volterra and Fredholm integral equations. By employing the CESTAC method in conjunction with the CADNA library, it becomes possible to automatically identify the optimal discretization step, the most accurate numerical approximation, and the associated computational error. Moreover, this framework is capable of detecting several types of numerical instabilities including self-validation, branching, intrinsic, and cancellation instabilities that typically remain unnoticed when using standard floating-point arithmetic. A fundamental theorem of the CESTAC method is also established, proving that the number of common significant digits between the exact and approximate solutions is equivalent to that between two successive approximations. This result yields a novel adaptive stopping criterion, which effectively replaces traditional termination conditions based solely on absolute error estimates.

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