Numerical methods for differential equations, collocation and spline techniques, fractional calculus, and mathematical modelling of nonlinear physical and engineering systems.

Dr. Shelly Arora is an Associate Professor in the Department of Mathematics at Punjabi University, Patiala, Punjab, India. She is an accomplished researcher in applied and computational mathematics, with a strong focus on numerical methods for differential equations, collocation techniques, spline methods, reaction–diffusion systems, fractional differential equations, and mathematical modelling of physical and engineering processes. She has successfully guided 8 Ph.D. scholars to completion and currently supervises 4 registered Ph.D. students, along with completing two funded research projects and one ongoing project. Dr. Arora has published extensively in high-impact international journals, with more than 45 research articles and several book chapters with reputed publishers, including Wiley and River Publishers. She has received multiple best paper awards at national and international conferences, including recognition from SEAM (USA). An active member of leading mathematical societies in India and abroad, she has delivered numerous invited talks and presented her work at prestigious conferences worldwide. Her contributions significantly advance numerical analysis, applied mathematics, and interdisciplinary mathematical modelling. Reference: An Implicit Hybrid Numerical Scheme to Study  Non-Linear Singularly Perturbed Boundary Value Problems Non-linear singularly perturbed boundary value problems are studied  numerically using an implicit hybrid numerical technique. The space direction is discretized using cubic and quintic Hermite splines. The time direction is discretized using an implicit weighted finite difference technique. The proposed technique is found to be unconditionally stable. The rate of convergence is found to be of order h r +?t 2 . The proposed hybrid technique is computationally efficient to be applied to different types of non-linear singularly perturbed boundary value problems. It gives numerical results for wide range of parameters.