Numerical analysis of partial differential equations

Course unit code

В.2.2

Course unit title

Basic Professional

Name(s), surname(s) and title of lecturer(s)

Alexander Starchenko, PhD, Professor

Semester

2

ECTS credits

6

Working hours

Contact hours

lectures

32

labs

32

Self-study

152

Total

216

Work placement

Laboratory works in Computer class

Prerequisites

It is assumed that the students have mastered the following disciplines "Mathematical analysis", "Differential Equations", "Partial Differential Equations", "Theory of Probability", "Numerical Methods of approximate calculations" and "Computer Sciences".

Language of instruction

English (Russian)

Objectives of the course

Learning outcomes

A student’s assessments methods

This course is intended for training Masters in Math to apply mathematical methods and modeling technique in their professional work.

This course is intended to give experience in the application of knowledge for development of the theoretical foundations of the methods of computational mathematics, for formation of practical skills development of numerical algorithms, for organization of computational experiment on the computer, for presentation of the results of calculations.

In mastering the subject of Numerical analysis of PDEs the student will acquire the following knowledge: finite-differencing, finite-volume and finite element approaches for numerical solution of PDEs.

The course helps to form and consolidate the following professional skills:

- to be able to get into a stated problem;

- to be able to formulate and analyze the result;

- to be able to correctly choose and use an appropriate mathematical language in a required subject area;

- to understand the principal idea that the fundamental knowledge in Mathematics forms the bases for modern Computer Sciences.

The current control of mastering the discipline includes three individual task and four reports on the labs.

The final control – exam.

Teaching methods

Lectures, Labs

List of Topics

Topic title

Contact hours

Assignments and independent study hours

Introduction.

2

Finite difference schemes for elliptic equations

8

Individual task 1

Jacobi method and SOR method for solving of difference equations

8

Lab 1

Finite difference schemes for heat equation

8

Lab 2

Finite difference schemes for hyperbolic equation

4

Individual task 2

Quadrature method for solving integral equations

6

Lab 3

Convection-diffusion equation and its properties

6

Basic finite-difference approximations of the diffusion-convection equation

6

Individual task 3

Finite Volume Method

10

Lab 4

Finite Volume Method on unstructured mesh

2

Finite Element Method

4

64

exam

Assessment requirements

In during the semester  70 points

Assessment criteria

Each lab 10 points and test 10 points

The composition of final accumulative mark

Exam 30 points.

Examination ticket consists of two theoretical questions (10x2=20) and one exercise (10x1=10).

Author of the course

Alexander Starchenko