# Numerical Solution of Differential Equations

• ECTS credits10
• Teaching semesterSpring
• Course codeMAT260
• Number of semesters1
• LanguageEnglish
• Resources

Spring

### Objectives and Content

Objectives:

The course deals with the numerical solution of differential equations and systems of non-linear equations.

Content:

Multistep methods as well as Runge-Kutta method for timedependent problem will be examined. Covergence, order and stability properties will be analysed. For boundary value problems we will have a look at finite difference, finite element and spectral methods.

For solving system of non-linear equations we will study fixpoint iteration and Newton's method, and discusse their convergence properties.

### Learning Outcomes

On completion of the course the student should have the following learning outcomes defined in terms of knowledge, skills and general competence:

Knowledge

The student

• has knowledge of state-of-the-art numerical methods in the field.
• Knows the convergence conditions for the different methods.
• Knows which order the different methods have and what exactly the term order means.
• Understands the concept of stiff differential equations, A-stability and stability domain for the different numerical schemes.
• Knows different spatial discretization schemes, such as: finite differences, finite elements and spectral methods.

Skills

The student

• is able to used the methods in numerical calculations. That is; to be able to implement them on a computer.
• is able to analyse the order of a numerical method.
• Understands the possibilities and the limitations of the different methods.

General competence

The student

• is able to make intelligent choices of method for specific problems
• converses easily and unforced about topics such as pros and cons in explicit vs implicit methods

### Required Previous Knowledge

MAT131 and MAT160

### Recommended Previous Knowledge

MAT160 Scientific computing I

Excercises

### Forms of Assessment

Due to coronavirus situation the exam spring semester 2020 will be digital oral examination. Exercises might be graded and included in the final grade. Grading scale Pass/Fail instead of A-F

### Examination Support Material

Non- programmable calculator, according to model listed in faculty regulations.

The grading scale used is passed/fail.