# Numerical Analysis

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• Parabolic Equations:

• Functions as first class objects

• Inheritance

• Explicit and implicit finite difference approximations to one – method

• Hyperbolic Equation:

• Characteristic method

• Finite difference solution of second order wave equation

• Elliptic equations:

• Improvement of accuracy

• Techniques near curved boundaries

• Consistency and stability analysis

• Convergence

• Finite difference method in polar coordinates

• Methods to accelerate the convergence

• Finite element method:

• Galerkin formulation

• Dirichlet and Neumann problems

• One and two dimensional elements

• Types of integral formulations

• Relative stability and intervals of stability

• Absolute stability

• Boundary value problems

• Eigenvalue problems

• Initial value problems

• Multistep methods (explicit and implicit)

• Predictor- corrector methods

• Runge-Kutta methods

• Shooting methods

• Stability analysis

• Zero stability