Weekly Hours: 5
ECTS Credits: 6
Course Homepage: http://ecourse.uoi.gr/course/view.php?id=1731
Description: The initial value problem (IVP) for ordinary differential equations: Existence and uniqueness of solutions, examples of non-existence and non-uniqueness of solutions. Differential equations of special form: linear, Bernoulli, Riccati, homogeneous, and equations of separable variables. Linear systems of differential equations. Numerical methods for initial value problems: Euler s method: stability and consistency properties and error estimates. Runge-Kutta methods: solvability, stability and consistency properties, and error estimates. Multistep methods: stability and consistency properties, and error estimates. Advantages and drawbacks of Runge-Kutta and multistep methods. The two-point boundary value problem: existence, uniqueness and smoothness of solutions.