About the Workshop

This workshop is designed to provide an in-depth exploration of advanced numerical techniques for solving ordinary differential equations (ODEs) and partial differential equations (PDEs), which frequently arise in a wide array of scientific and engineering disciplines. Applications span diverse areas such as wave propagation, heat conduction, acoustic and electromagnetic waves, fluid dynamics, chemical kinetics, and other physical phenomena governed by complex mathematical models. Analytical solutions to such differential equations are often unattainable due to the inherent challenges posed by non-linearity, limited regularity of solutions, and the complex structure of real-world problems. Even in cases where the existence and uniqueness of solutions are theoretically guaranteed, the actual construction of closed-form solutions remains elusive. Hence, the necessity for robust numerical methods becomes paramount.

This workshop aims to introduce participants to a variety of classical and modern numerical approaches for solving both linear and non-linear ODEs and PDEs. A significant focus is placed on the discretization techniques that underpin these methods, such as: Finite Difference Methods (FDM), Finite Element Methods (FVM), Finite Volume method, Discontinuous Galerkin Methods (DGM) Recognizing the transformative impact of data-driven techniques in recent years, the workshop also introduces participants to Machine Learning (ML), Deep Learning (DL), and Physics-Informed Neural Networks (PINNs). These modern tools integrate physical laws (in the form of differential equations) into neural network architectures, allowing for the approximate solution of PDEs where traditional methods may struggle, particularly in high dimensions or data-scarce regimes. 

The workshop is specifically tailored for doctoral students (Ph.D. scholars) and postdoctoral researchers who are engaged in the mathematical modeling and numerical analysis of complex systems. Workshop is open to faculty/students from all institutes, colleges and universities of India. Industry personnel working in the concerned/allied disciplines may also apply. It is designed to equip participants with both theoretical foundations and practical skills to apply these numerical methods effectively in their research.

About TIET 

The Thapar Institute of Engineering and Technology (TIET) is one of India's oldest and finest educational institutions, which provides a steady source of highly skilled talent to the nation as well as overseas. Founded in 1956 with a campus spread across sprawling 250 acres, Thapar Institute of Engineering & Technology, located in Patiala, has been a pioneer in engineering education, research and innovation. Rated amongst the top ranked innovation-driven private universities and technical institutes in the country, Thapar Institute of Engineering & Technology has been accredited with an ‘A++' grade by the National Assessment and Accreditation Council (NAAC).