Topic of Research Seminar: Galerkin and Petrov-Galerkin Finite Element Method for Integer and Fractional-Order Differential Equations

Abstract: Differential equations are fundamental tools for modeling time-dependent and stationary processes across science and engineering. In particular, fractional differential equations have gained increasing attention due to their ability to capture memory and nonlocal effects in complex systems. In this seminar, we present spline-based Galerkin and Petrov-Galerkin finite element methods for solving both integer and fractional-order differential equations. Using B-spline functions as both shape and test functions and employing a four-point Gauss-Legendre quadrature rule to efficiently handle complex integrals, the framework provides accurate, stable, and efficient numerical approximations for a variety of models, including wave propagation and transport phenomena. Several benchmark problems are explored to demonstrate the effectiveness of the methods. These approaches offer flexible and reliable computational tools for a wide range of real-world applications

Subject Field of Topic: Differential Equation

Name of Speaker: Dr. Shams Ul Arifeen

Professorial Rank of Speaker: Assistant Professor (Mathematics Dpt.) SNS

Affiliation of Speaker: School of Natural Sciences (SNS – NUST)

Date and Venue: (Wednesday) 28 January, 2026, 03:30 PM, Room # 403 Old Building, School of Natural Sciences (SNS), NUST Islamabad