Numerical solution of Partial Differential Equations, Differential methods for parabolic and hyperbolic partial differential equations, one space dimension, two space dimension, Variable coefficients problem, non linear equations.
Unit II:
II
15.00
Differential methods for elliptic partial differential equations, general second order linear equations, quasi-linear elliptic equations, multi grid methods.
Unit III:
III
15.00
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.
Unit IV:
IV
15.00
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.
Unit V:
V
15.00
Dynamical systems, Bifurcation and stability of dynamical systems, one parameter bifurcation of continuous time dynamical systems, Hopf bifurcation in reaction – diffusion systems.
Essential Readings:
Fourier and Wavelet Analysis : G. Bachman, L. Narici and E. Beckenstein: Springer
Methods for PDEs and Frontiers in Numerical Analysis : J.E. Blawey, A.W. Craig : Springer
Theoretical Numerical Analysis : K. Atkinson, and W. Hay : Springer
