# Scientific Computing (MAE848A)

### General

School School of Science Department of Mathematics Undergraduate MAE848A 8 Scientific Computing Lectures (Weekly Teaching Hours: 3, Credits: 6) Special Background - Greek Yes (in English) See eCourse, the Learning Management System maintained by the University of Ioannina.

### Learning Outcomes

Learning outcomes In most scientific disciplines, the integration of computers has defined new directions to perform research and has offered unprecedented potential to solve complicated problems. Combined with theory and experimentation, computational analysis is nowadays considered an integral part of science and research. The main objective of the course is to familiarize the student with computational techniques that find application in the solution of ordinary and partial differential equations. In the context of this laboratory course, the student will gain access to the programming languages Matlab/Octave and Python, which are widely used to perform scientific calculations. Computational methods to be developed and implemented in PCs will significantly increase the skills and prospects of integrating graduates into the modern scientific and work environment. Starting from the mathematical modeling of problems of Mechanics and Applied Mathematics in general, and by synthesizing information from numerical analysis and numerical solution of ordinary and partial differential equations, students will acquire crucial knowledge in solving mathematical problems by computational means. Specifically, the objectives of the course are: Familiarity with the Matlab/Octave and Python programming languages to implement numerical methods, solve mathematical problems and graphically design the numerical results Apply numerical derivation using the Finite Difference method Analysis of the numerical schemes resulting from the Finite Difference method Solving ordinary differential equations using one-step and multi-step methods Solving parabolic and elliptic Partial Differential Equations with the Finite Difference Method Theoretical analysis of the Finite Element method Solving parabolic and elliptic Partial Differential Equations with the Finite Element method. The course aims to enable the student to: Search, analyze and synthesize data and information, using the available technologies Work autonomously Work in a team Promote free, creative and inductive thinking.

### Syllabus

• Initial Value Problems
• Boundary Value Problems
• Finite Difference method
• Equations of Difference
• Shooting methods and Method of undetermined coefficients
• One-step Methods (Euler, Taylor, Runge-Kutta)
• Finite Element Method (Galerkin).

### Teaching and Learning Methods - Evaluation

Delivery

In the laboratory

Use of Information and Communications Technology Use of scientific computing software packages
Teaching Methods
Lectures 39
Study of bibliography 39
Laboratory exercises 39
Home exercises (project) 33
Course total 150
Student Performance Evaluation
• Weekly assignments
• Final project
• Written examination at the end of the semester

### Attached Bibliography

See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:

• Numerical Methods for Ordinary Differential Equations, 2 Edition, G.D. Akrivis, V.A. Dougalis, 2012 (in Greek).
• A Primer on Scientific Programming with Python, H. P. Langtangen, Springer-Verlag Berlin Heidelberg, 5 Edition, 2016.
• Programming for Computations- MATLAB/Octave, S. Linge, H. P. Langtangen, Springer International Publishing, 2016 (in Greek).
• The Mathematical Theory of Finite Element Method, S. C. Brenner, L. R. Scott, Springer-Verlag, New York, 2008.
• Automated Solution of Differential Equations by the Finite Element Method, A. Logg, K.-A. Mardal, G. N. Wells, Springer-Verlag Berlin Heidelberg, 2012.