Numerical Analysis: Numerical Methods for Differential Equations

<p>The course provides a basic introduction to numerical analysis for differential equations. This includes design, analysis, implementation and application of numerical methods for initial value problems, boundary value problems and various types of partial differential equations.</p><p>The course treats:</p> <ul> <li>Methods for time integration: Euler’s method, the trapezoidal rule. Multistep methods: Adams' methods, backward differentiation formulae.</li> <li>Explicit and implicit Runge-Kutta methods.</li> <li>Error analysis, stability and convergence.</li> <li>Stiff problems and A-stability. Error control and adaptivity.</li> <li>The Poisson equation: finite differences and the finite element method.</li> <li>Elliptic, parabolic and hyperbolic problems.</li> <li>Time dependent partial differential equations: numerical schemes for the diffusion equation.</li> <li>Introduction to difference methods for conservation laws.</li> </ul>