MSc (Mathematics and Computing) Programme:Numerical Methods for Partial Differential Equations

Semester I

Real Analysis – I
Linear Algebra
Complex Analysis
Fundamentals of Computer Science and C Programming
Discrete Mathematical Structure
Differential Equations


Semester II

Real Analysis –II
Advanced Abstract Algebra
Computer Oriented Numerical Methods
Data Structures
Data Based Management Systems
Operating Systems


Semester III

Topology
Computer Based Optimization Techniques
Computer Networks
Mechanics
Seminar


Semester IV

Functional Analysis
Dissertation


Numerical Methods for Partial Differential Equations

Parabolic equations: Numerical solutions of parabolic equations of second order in one space variable with constant coefficients –two and three levels explicit and implicit difference schemes, truncation errors and stability.

Numerical solution of parabolic equations of second order in two space variable with constant coefficients-improved explicit schemes, Larkin modifications, implicit methods, alternating direction implicit (ADI) methods.

Difference schemes for parabolic equations with variable coefficients in one and two space dimensions. Difference schemes in spherical and cylindrical coordinate systems in one dimension.

Hyperbolic Equations: Numerical solution of hyperbolic equations of second order in one and two space variables with constant and variable coefficients-explicit and implicit methods. ADI methods, Difference schemes for first order equations.

Elliptic Equations: Numerical solutions of elliptic equations, approximations of Laplace and biharmonic operators. Solutions of Dirichlet, Neumann and mixed type problems with Laplace and Poisson equations in rectangular, circular and triangular regions, ADI methods.

Finite Element Method: Introduction to FEM, FEM for Laplace, Poisson, heat flow and wave equations.

Laboratory Work