The aim of studying and bibliography

The main aim of study: To acquaint students with the basic numerical methods of solving differential equations

The general information about the module: The module contains content in the field of methods of numerical solution of stiff systems of ordinary differential equations, boundary value problems for ordinary differential equations

others: Literatura wykorzystywana podczas zajęć zostanie podana po wybraniu tematyki zajęć.

Bibliography required to complete the module

Bibliography used during lectures

1	D. Kincaid, W.Cheney	Analiza numeryczna	WNT, Warszawa .	2006
2	Z. Fortuna, B. Macukow, J. Wąsowski	Metody numeryczne	WNT, Warszawa.	2002

Bibliography used during classes/laboratories/others

1	T. Ratajczak	Metody numeryczne. Przykłady i zadania	Wydawnictwo politechniki Gdańskiej.	2006
2			.

Bibliography to self-study

1

M. Dryja, J. i M. Jankowscy

Przegląd metod i algorytmów numerycznych

WNT, Warszawa.

1988

Basic requirements in category knowledge/skills/social competences

Formal requirements: Completed mathematical analysis courses, algebra, differential equations and numerical methods.

Basic requirements in category knowledge: Basic knowledge of mathematical analysis and matrix calculations, differential equations and numerical methods

Basic requirements in category skills: Ability to solve selected problems in the field of linear algebra, differential and integral calculus, differential equations and numerical methods.

Basic requirements in category social competences: It can appropriately determine the priorities for the realization of one's own or other tasks

Module outcomes

MEK	The student who completed the module	Types of classes / teaching methods leading to achieving a given outcome of teaching	Methods of verifying every mentioned outcome of teaching	Relationships with KEK	Relationships with PRK
01				K_W02++ K_W04+ K_W06+ K_K01+	P6S_KK P6S_WG P6S_WK
02				K_W05+++ K_K01+	P6S_KK P6S_WG
03				K_W01+ K_W02+ K_W03+ K_W05+ K_U01+++ K_K01+	P6S_KK P6S_UK P6S_WG P6S_WK

Attention: Depending on the epidemic situation, verification of the achieved learning outcomes specified in the study program, in particular credits and examinations at the end of specific classes, can be implemented remotely (real-time meetings).

The syllabus of the module

Sem.	TK	The content	realized in	MEK
6	TK01	Mathematical modeling and numerical calculations.	W1	MEK01 MEK02
6	TK02	Initial problem for systems of ordinary differential equations. Linear multi-step methods for systems of ordinary differential equations. Backward Differentiation Formulas (Gear's Methods). Nordsik's methods.	W2-W5, C1,C2	MEK01 MEK02 MEK03
6	TK03	Numerical integration of stiff systems of ordinary differential equations. The concept of a stiff problem. Absolute stability of numerical methods. Implementation of implicit linear multi-step methods.	W6-W11, C3-C6	MEK01 MEK02 MEK03
6	TK04	Boundary problems for ordinary differential equations. Shooting methods: simple shooting method, multiple shoting method.	W12-W16, C7,C8	MEK01 MEK02 MEK03
6	TK05	Finite difference method. Methods of constructing differential schemes: method of replacing derivatives with finite differences, method of indefinite coefficients, integro-interpolation method. Finite difference method for nonlinear ordinary differential equations.	W17-W24, C9-C13	MEK01 MEK02 MEK03
6	TK06	Galerkin method. Constructing mesh schemes using the finite element method. Basic concepts of the mesh method.	W25-W30, C14,C15	MEK01 MEK02 MEK03

The student's effort

The type of classes	The work before classes	The participation in classes	The work after classes
Lecture (sem. 6)		contact hours: 30.00 hours/sem.	complementing/reading through notes: 3.00 hours/sem. Studying the recommended bibliography: 2.00 hours/sem.
Class (sem. 6)	The preparation for a Class: 5.00 hours/sem. The preparation for a test: 5.00 hours/sem.	contact hours: 15.00 hours/sem.	Finishing/Studying tasks: 5.00 hours/sem.
Advice (sem. 6)
Credit (sem. 6)

The way of giving the component module grades and the final grade

The type of classes	The way of giving the final grade
Lecture	Written work (tasks)
Class
The final grade	Average grade: written work (80%), class work (20%)

Sample problems

Required during the exam/when receiving the credit
(-)

Realized during classes/laboratories/projects
(-)

Others
(-)

Can a student use any teaching aids during the exam/when receiving the credit : no

The contents of the module are associated with the research profile: yes

1	B. Datsko; M. Kutniv	Explicit numerical methods for solving singular initial value problems for systems of second-order nonlinear ODEs	2024
2	E. Özkan; D. Strzałka; A. Włoch; N. Yilmaz	On Doubled and Quadrupled Fibonacci Type Sequences	2024
3	N. Khomenko; A. Kunynets; M. Kutniv	Algorithmic Realization of an Exact Three-Point Difference Scheme for the Sturm–Liouville Problem	2023
4	N. Khomenko; A. Kunynets; M. Kutniv	Three-Point Difference Schemes of High Order of Accuracy for the Sturm–Liouville Problem	2023
5	P. Jaśkiewicz; B. Kozicki; A. Włoch; J. Zieliński	The Impact of the Covid-19 Pandemic and the War Between Russia and Ukraine on Electricity Prices in Selected European Countries in 2022 in Terms of Economic Security	2023
6	M. Król; M. Kutniv	New Algorithmic Implementation of Exact Three-Point Difference Schemes for Systems of Nonlinear Ordinary Differential Equations of the Second Order	2022
7	R. Grabowski; B. Kozicki; S. Mitkow; A. Włoch	Impact of Covid-19 Pandemic on Economic Security - Multidimensional Analysis of Real Estate Market Across Poland	2022
8	U. Bednarz; A. Włoch; M. Wołowiec-Musiał	New Types of Distance Padovan Sequences via Decomposition Technique	2022
9	B. Datsko; A. Kunynets; M. Kutniv; A. Włoch	New explicit high‐order one‐step methods for singular initial value problems	2021
10	D. Bród; A. Włoch	(2,k)-Distance Fibonacci Polynomials	2021
11	D. Strzałka; A. Włoch; S. Wolski	Distance Fibonacci Polynomials by Graph Methods	2021
12	E. Özkan; A. Włoch; N. Yilmaz	On F3(k,n)-numbers of the Fibonacci type	2021
13	G. Harmatiy; B. Kalynyak; M. Kutniv	Uncoupled Quasistatic Problem of Thermoelasticity for a Two-Layer Hollow Thermally Sensitive Cylinder Under the Conditions of Convective Heat Exchange	2021
14	A. Włoch; I. Włoch	On some multinomial sums related to the Fibonacci type numbers	2020
15	B. Datsko; A. Kunynets; M. Kutniv; A. Włoch	A new approach to constructing of explicit one-step methods of high order for singular initial value problems for nonlinear ordinary differential equations	2020
16	B. Datsko; M. Kutniv; A. Włoch	Mathematical modelling of pattern formation in activator–inhibitor reaction–diffusion systems with anomalous diffusion	2020
17	H. Czyż; T. Jasiński; A. Włoch	A Statistical Method for Calculating the Velocity of Acoustic Waves in Extreme Conditions	2019
18	H. Czyż; T. Jasiński; A. Włoch	Separation of Cells from Plasma by Means of Ultrasonics	2019
19	H. Czyż; T. Jasiński; A. Włoch	The Application of the Special Functions to Solving Physical Problems	2019