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