Numerical Analysis II

Syllabus

• Numerical integration: elementary and composite quadrature formulas.
• Orthogonal polynomials and Gaussian quadrature methods.
• Numerical treatment of special integrands.
• Initial value problems for ordinary differential equations: explicit and implicit Euler methods.
• Consistency, stability, and convergence of numerical methods for ODEs.
• Inheritance of asymptotic stability under numerical discretisation.
• Explicit Runge–Kutta methods for initial value problems.
• Linear multistep methods: order of the method, root condition, and stability.
• Finite difference discretisation of basic elliptic and parabolic partial differential equations on equidistant grids.
• Solution techniques based on Fourier methods.
• The Fast Fourier Transform algorithm and its numerical role.