NCMW - Numerical Methods for Partial Differential Equations (2024)

Venue: Indian Institute of Petroleum and Energy (IIPE), Visakhapatnam

Dates: 16 Dec 2024 to 27 Dec 2024

The workshop is on numerical methods for ordinary and partial differential equations (ODEs & PDEs) like those arising in science and engineering applications, such as wave, heat and sound propagation, fluid flow, chemical kinetics, etc. Generally, the solutions of differential equations are quite challenging, admit to limited regularity, may have complex structures in their form, and are highly nonlinear. It may not be possible to obtain an analytical solution even if we know the theoretical existence and uniqueness of the solution. Numerical methods offer a way to discretize the differential equations and then solve them. Thus, this workshop introduces some important numerical methods for linear and non-linear ordinary and partial differential equations and various numerical discretization techniques for their solution. We mainly focus on the construction of finite difference (FDM), finite volume methods (FVM), and discontinuous Galerkin methods (DGM) and their numerical convergence for the various nonlinear ODEs & PDEs. Higher-order methods are essential for wave propagation phenomena. Here, we discuss modern methods like WENO and DG for various applications of wave propagation such as hyperbolic conservation laws, Hamilton-Jacobi equation, and Convection-Diffusion-Dispersive type nonlinear PDEs. Machine learning and Deep learning techniques are quite popular nowadays, thus this workshop intends to introduce Machine Learning, Deep Learning, and Physics Informed Neural Networks (PINNs) and their applications to solve partial differential equations. This workshop is intended for PhDs and Postdocs so that they can learn these techniques and use them in their research.