Linear Algebra, Differential Equations, Linear Algebra and its Applications to Fractional/Integer Order Differential Equations

About the Project

Linear Algebra and Differential Equations are both challenging subjects at a mathematical level and crucial in many ways for science and engineering. In addition, linear algebra methods are an essential part of the methodology commonly used to solve differential equations and systems. The main of this project is to find the invariant subspaces for the differential operators. The obtained linear spaces will be helpful for deriving the exact solutions in the finite separable form for nonlinear partial differential equations. In this project, we can investigate various types of linear spaces for quadratic and cubic differential operators, which are essential for deriving analytical solutions for fractional-order nonlinear partial differential equations due to unusual or nonstandard properties of fractional order derivatives. In addition, we can find various dimensional linear spaces in different types for differential operators. Also, we can discuss the linear spaces/solution spaces and their properties with their corresponding differential operators. The invariant subspace method generates many interesting exact solutions to nonlinear evolution equations in mechanics and physics.

Department and Campus

Department of Mathematics, School of Physical Sciences, Coimbatore

Skillsets Preferred from Applicants

Good Percentage in B.Sc., and M.Sc.(Mathematics/Applied Mathematics) or CSIR-UGC- NET or GATE or SET.