Boundary value problems with or without eigenvalues: shooting method for nonlinear problems, finite difference methods for boundary value problems, etc.

Numerics for ordinary differential equations (IVPs and BVPs):Initial Value problems: Euler's method, Higher order Taylor's method, Runge-Kutta method, stability and convergence. Numerics for parabolic and hyperbolic partial differential equations : basic finite difference approximation of parabolic and hyperbolic pde, truncation error, convergence through stability and consistency, higher order and compact approximations, application to some of the benchmark problems from incompressible flows pde models - gravity waves and their occurrence in atmosphere, critical levels and their significance, the energy and momentum transfer double diffusive convection and its solutions, finger and other instabilities.Īpplications of Lie group to Differential Equations: Lie group, Transformation group, applications of Lie group to nonlinear ODE and nonlinear PDE Examples and their applications in various fields.Īpplications of IBVPs:ode model - human immune system, system of equations, phase plane analysis and interpretation, two extreme cases.

Green’s functions for a ball and for an upper half plane.įirst order nonlinear equations: First order partial differential equations: Introduction to PDE, solving linear, semilinear, quasilinear and fully nonlinear first order equations by using the method of characteristics. Professor – Centre for Nonlinear Dynamics, Bharathidasan University (ML)Įlliptic partial differential equations:Gauss-Green theorem, Integration by parts formula, fundamental solution for Laplace equation, solving Poisson equation in Rn, Harnack’s inequality, Green’s functions, representation formula for the solution of boundary value problem by using Green’s function. Professor, IIT Madras (YVSSS), IIT Hyderabad Bharathiar University, Coimbatore, Tamil Naduĭean – TIFR Centre for Applicable Mathematicsįormer Professor, Bharathiar University (PK)

Meshfree methods math.iit