Department of Mathematics


Faculty in the Department are involved in a wide range of research representing the various disciplines (Differential Equations, Differential Inequalities and Numerical Analysis and Algebra ) and also newly emerging interdisciplinary areas.

Singular perturbation problems for differential equations occur in many branches of applied mathematics. The existence, uniqueness, stability and asymptotic behaviour of solution of these problems have been extensively studied by many researchers. Various perturbation methods to obtain asymptotic expansion of solution and numerical methods are also available in the literature. Solutions of these problems, in general, exhibit certain non-uniform behaviour on the domain of definition of the equations. Because of this, classical numerical methods fail to yield good approximations to solutions of these problems.

For the past three decades a good number of research articles which present various numerical methods have been appearing in the literature. These methods include Boundary Value Technique, Schwarz method, Shooting method, Booster method, Fitted operator method, Fitted mesh method, Initial Value Technique, Collocation method and Finite Element method. Most of these methods are used to find numerical solutions for singularly perturbed ordinary differential equations of second order. Only a few authors considered higher order equations. The same statement is true for differential equations involving two or more small parameters. Some authors used these methods to obtain numerical solutions for singularly perturbed partial differential equations of parabolic and elliptic type.

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