Numerical Solutions of Ordinary Differential Equations
Basic concepts. Need and usefulness of the numerical solution of ordinary differential equations. Initial value problems. Single-step methods. Taylor’s series method. Runge-Kutta methods. Error estimates. Multi-step methods. Adams-Bashforth methods. Predictor-corrector methods. Adams-Moulton methods. Adaptive stepsize control. Modified predictor-corrector methods. Methods for systems of ordinary differential equations. Methods for ordinary differential equations of higher order. Methods for second order ordinary differential equations of a particular form. Numerov’s method. Transmission errors. Total error. Convergence. Numerical stability. Stiff equations. Theory of Butcher’s trees. Boundary value problems. Examples. Applications.
Laboratory exercises using the mathematical computing environment Matlab (and/or the General Public License-GNU Octave) to implement the course's methods and algorithms.