Advanced Numerical Methods (Optional Paper)
Numerical solution of Partial Differential Equations, Finite Difference method for parabolic and hyperbolic partial differential equations, one space dimension, two space dimension, Variable coefficients problem, non linear equations.
Finite Difference method for elliptic partial differential equations, general second order linear equations, quasi-linear elliptic equations.
Wavelet analysis :Wavelets, Haar Wavelets, continuous Wavelet transforms, discrete Wavelet transforms, multi resolutions Wavelet transforms, Algebra and geometry of Wavelet – matrices, one dimensional wavelet systems.
Finite Element Methods & Bifurcation Theory. Basics of finite element methods, Discretization, error estimates of finite element interpretations, generalized finite element method, finite element limit analysis.
Dynamical systems, Bifurcation and stability of dynamical systems, one parameter bifurcation of continuous time dynamical systems, Hopf bifurcation in reaction – diffusion systems.
1. Fourier and Wavelet Analysis : G. Bachman, L. Narici and E. Beckenstein: Springer
2. Methods for PDEs and Frontiers in Numerical Analysis : J.E. Blawey, A.W. Craig : Springer
3. Theoretical Numerical Analysis : K. Atkinson, and W. Hay : Springer
1. Computational Methods for PDEs : M.K. Jain, S.R.K. Iyengar, R.K. Jain : Wiley Eastern.
2. Numerical Methods Problems and solutions, Jain ; Iyengar
3. Numerical Methods for Engineers, Chapra,Steven C
