Singularly Perturbed Problems, Semi-conductor Device Models, Periodic Boundary Value Problems in Oceanography and Machine Learning Techniques

About the Project

A differential equation with a small positive parameter multiplying at the highest derivative term subject to boundary conditions belongs to a class of problems known as Singular Perturbation Problems (SPPs). Singularly perturbed boundary value problems appear in many branches of applied mathematics. The solution of singular perturbation problems has non-uniform behavior, that is, there are thin layer (boundary layer region) where the solution varies rapidly while away from the layer (outer region) the solution behaves regularly and varies slowly. Often these mathematical problems are extremely difficult (or even impossible) to solve exactly and in these circumstances, approximate solutions are necessary. Standard numerical methods which have been known to be effective for solving most problems that arise in applications have failed when applied to the singular perturbation problems, that is, classical numerical methods fail to yield good approximations for the solutions of these problems. Therefore a need arises to construct and analysed special type of computational methods to get a satisfactory solution on the entire region (boundary layer region and
outer region) where a singular perturbation problem is defined.

Department and Campus

Department of Mathematics, School of Physical Sciences, Coimbatore

Skillsets Preferred from Applicants

Computational and algorithmic skill is necessary