报告问题 (Title): Stable Distributed Gauss Quadrature Scheme for Distributed Order Mathematical Models (漫衍阶数学模子的稳固漫衍高斯正交名堂)

报告人 (Speaker)： Vineet Kumar Singh 教授（Indian Institute of Technology (Banaras Hindu University) 大学）

报告时间 (Time)：2024年5月21日 (周二) 14:00

报告所在 (Place)：校本部GJ403

约请人(Inviter)：李常品、蔡敏

主理部分：理学院数学系

报告摘要：In this work, we designed a distributed-order Gauss-Quadrature scheme to approximate solutions for distributed-order mathematical models. Quadrature rules and their applications have been primarily noted with respect to special functions like Legendre, Bernstein, Hermite, and others. In this work, we establish a numerical scheme based on the given weight function in the proposed mathematical models. The designed scheme depends entirely on a single input function known as the distributed-order weight function, alongside the development of an orthogonal generating polynomial (OGP). The proposed problem has been solved numerically with the help of the OGP Gauss Quadrature rule along with an operational matrix based on the designed OGP technique. Theoretical error bounds, stability analysis, and efficiency are rigorously investigated and a comprehensive set of examples are provided to validate the reliability and accuracy of the proposed numerical scheme.