Introduction: The initial value problem, Picard s Theorem, Euler s method, basic concepts, consistency, stability, error estimates, influence of machine errors. One-step Methods: General theory, consistency, stability, error estimates, implicit (complex) methods, applications to systems of equations. Runge-Kutta Methods: Construction and algorithmic formalization, study of convergence, stability, error estimates. Multi-step Methods: Construction and basic concepts, the root criterion, study of convergence, stability and error estimates, algorithmic formalization. Boundary Value Problems: Introduction to basic concepts, convergence theorems, stability, error estimates, the shooting method, the Sturm-Liouville problem, introduction to finite difference and finite element methods for ordinary and partial differential equations.
- Teacher: Κωνσταντινος Χρυσαφινος
ECTS : 6
Language : el