Numerical Methods

Course content

Numerical solution of Ordinary Differential Equations (ODE): Initial value problems; Runge-Kutta methods; Adaptive stepping; Systems of ODEs; Higher order ODEs; Boundary value problems. Numerical solution of partial Differential Equations (PDE): Finite volume method; Numerical solution using triangular grids; Finite difference method; Model equations; Finite difference approximations; Convergence and stability analysis of finite difference equations; Numerical solutions of parabolic PDEs; Elliptic PDEs; Hyperbolic PDEs.