MULTIRATE LINEAR MULTISTEP METHODS FOR THE SOLUTION OF SYSTEMS OF ORDINARY DIFFERENTIAL EQUATIONS

In certain systems of Ordinary Differential Equations, some components of the solution vary more rapidly than others. In this thesis numerical methods designed to solve such problems are considered. These methods are based on linear multistep methods but instead of integrating all components with the same stepsize, slower components are integrated with a larger stepsize than that used on the fast. The convergence of these methods under suitable conditions is established and their absolute stability properties are discussed. A code implementing these methods is included along with the results of some numerical experiments which show their effectiveness in solving certain types of problems.