Faculty Research

Many real-world systems arising in science, engineering, and finance exhibit behaviour across multiple scales, where small changes can produce significant effects. A central mathematical framework for understanding such phenomena is singular perturbation theory, which studies problems in which a small parameter leads to sharp transitions or rapid variations in the solution. These localized changes, often referred to as boundary or interior layers, present significant challenges for standard numerical methods.

A simple way to understand this is through a real-life analogy. Imagine driving on a highway where most of the road is smooth, but suddenly you encounter a sharp speed breaker or a rough patch. Although the irregularity is confined to a small region, it significantly affects the overall motion of the vehicle. Similarly, in singular perturbation problems, small regions with rapid changes can strongly influence the overall behaviour of the system.

Dr. Satpal Singh’s research focuses on developing robust and accurate computational techniques to address these challenges. By employing advanced discretization strategies, such as exponentially graded meshes, the numerical methods are specifically designed to capture sharp gradients efficiently. These approaches ensure that computational effort is concentrated in regions where the solution changes rapidly, leading to improved accuracy without excessive cost.