ΜΥ03 - Numerical Analysis

Information

Code : ΜΥ03

Type : Obligatory

Semester : 2

ECTS credits: 6

Course URL: https://eclass.hua.gr/courses/DIT154/

Expected Outcomes

The course belongs to the wider area of Scientific Computing. Scientific calculations are the basis for many fields and an important tool for the study of scientific problems arising from many sciences such as Physics, Chemistry, Biology, Economics etc. Most of these problems lead to the solution of a mathematical problem, for which either there is not always an analytical solution, or if there is it requires complex calculations. The course also includes the implementation of algorithms in a laboratory environment, based on the programming language Python.

Content

Errors in numerical calculaitons
-Representation of numbers in memory, rounding error,s propagating error.

Numerical solution of nonlinear equations
- Dividing method
- Fixed point problem
- Newton Rapshon method
- Cutting method
- Horner shape

Numerical methods for solving linear systems
- Gaussian elimination method
- Jordan elimination method
- Three-diagonal system solution
- Basic iterative methods

Numerical calculation of eigenvalues and eigenvectors
- Method of forces
- Reverse method of forces.

Approximation of functions
- Finite differences
- Interpolation polynomial

Numerical derivation and integration
- Types of numerical derivation for equidistant points
- Numerical derivation by the method of determinable factors
- Error in arithmetic derivation

Numerical solution of ordinary differential equations
- Euler method
- Taylor series method
- Numerical solution of ordinary differential equations with boundary conditions

Evaluation Means

Bibliοgraphy

-Applied numerical analysis - 3rd edition, P. Giannopoulou, A. Dimitriadis Δημητριάδης, S. Doukakis, C. Kilias, N. Matzakos Νίκος
-Numerical methods and applications for engineers, 4th edition, Sarris, I. - Karakasidis T.
-Numerical methods for engineers, 7th edition, Chapra S. - Canale R., F. Koutelieris editing