Erge Ideon "Rational spline collocation for boundary value problems"

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View all other units

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Date:

26.06.2013 - 11:15 to 13:15

Supervisor: Peeter Oja (dots., TÜ matemaatika instituut)
Opponents: Jaan Janno (prof., Tallinna Tehnikaülikool)
Natalja Budkina (Dr. math., Riga Technical University)

Summary:
Boundary value problems arise in several branches of scientific and engineering problems. Traditional methods for approximate solution of boundary value problems are finite difference method which only gives a discrete solution, and collocation method with polynomial splines. The latter one has been quite well studied. It is known, that in interpolation in some cases the rational splines may have better results compared to polynomial ones. In such circumstances, it is natural to pose the question about rational spline collocation method for boundary value problems. In recent years the shape preserving problems have been considered by several authors. Polynomial splines do not preserve the monotonicity or convexity. On the other hand, the linear/linear rational spline is constant or strictly monotone and the quadratic/linear rational spline is always convex (or concave). Therefore, it is a reasonable approximate solution only if the exact solution of the problem has same properties. The main purpose of the thesis is to study the linear/linear and quadratic/linear rational spline collocation method for boundary value problems and also compare them to quadratic and cubic spline cases, respectively. The collocation method with rational splines is, in nature, a nonlinear method because it leads to a nonlinear system with respect to the spline parameters. Also the rational spline interpolation has been studied because the results of rational spline collocation method are based on certain convergence properties of interpolating rational splines. Numerical examples support the obtained theoretical results.

Organizer:

Location:

J. Liivi Street 2, room 403

URL:

hdl.handle.net/10062/30349

Event category:

Defence

M	T	W	T	F	S	S
			1 Matti Vainio's exhibition "Findings \| Leiud" The Exhibition "The enchanting art of stone cutting. Morgenstern 250" Aarne Maasik’s Photos of Tartu Cathedral Estonia's National University 100: Photo exhibition “Put on Your Thinking Cap! The Hundred Faces of the University of Tartu”	2 Egon Urgard "Potential therapeutic approaches for modulation of inflammatory response pathways" Matti Vainio's exhibition "Findings \| Leiud" The Exhibition "The enchanting art of stone cutting. Morgenstern 250" Aarne Maasik’s Photos of Tartu Cathedral Estonia's National University 100: Photo exhibition “Put on Your Thinking Cap! The Hundred Faces of the University of Tartu”	3 Matti Vainio's exhibition "Findings \| Leiud" The Exhibition "The enchanting art of stone cutting. Morgenstern 250" Aarne Maasik’s Photos of Tartu Cathedral Estonia's National University 100: Photo exhibition “Put on Your Thinking Cap! The Hundred Faces of the University of Tartu”	4 Matti Vainio's exhibition "Findings \| Leiud" The Exhibition "The enchanting art of stone cutting. Morgenstern 250" Aarne Maasik’s Photos of Tartu Cathedral Estonia's National University 100: Photo exhibition “Put on Your Thinking Cap! The Hundred Faces of the University of Tartu”
5 Indrek Teino “Studies on aryl hydrocarbon receptor in the mouse granulosa cell model” Matti Vainio's exhibition "Findings \| Leiud" The Exhibition "The enchanting art of stone cutting. Morgenstern 250" Aarne Maasik’s Photos of Tartu Cathedral Estonia's National University 100: Photo exhibition “Put on Your Thinking Cap! The Hundred Faces of the University of Tartu”	6 Welcome Reception for International Staff and PhD Students Matti Vainio's exhibition "Findings \| Leiud" The Exhibition "The enchanting art of stone cutting. Morgenstern 250" Aarne Maasik’s Photos of Tartu Cathedral Estonia's National University 100: Photo exhibition “Put on Your Thinking Cap! The Hundred Faces of the University of Tartu”	7 Matti Vainio's exhibition "Findings \| Leiud" The Exhibition "The enchanting art of stone cutting. Morgenstern 250" Aarne Maasik’s Photos of Tartu Cathedral Estonia's National University 100: Photo exhibition “Put on Your Thinking Cap! The Hundred Faces of the University of Tartu”	8 Matti Vainio's exhibition "Findings \| Leiud" The Exhibition "The enchanting art of stone cutting. Morgenstern 250" Aarne Maasik’s Photos of Tartu Cathedral Estonia's National University 100: Photo exhibition “Put on Your Thinking Cap! The Hundred Faces of the University of Tartu”	9 Seminar focusing on SARS-CoV-2/COVID19 research Matti Vainio's exhibition "Findings \| Leiud" The Exhibition "The enchanting art of stone cutting. Morgenstern 250" Aarne Maasik’s Photos of Tartu Cathedral Estonia's National University 100: Photo exhibition “Put on Your Thinking Cap! The Hundred Faces of the University of Tartu”	10 Matti Vainio's exhibition "Findings \| Leiud" The Exhibition "The enchanting art of stone cutting. Morgenstern 250" Aarne Maasik’s Photos of Tartu Cathedral Estonia's National University 100: Photo exhibition “Put on Your Thinking Cap! The Hundred Faces of the University of Tartu”	11 Matti Vainio's exhibition "Findings \| Leiud" The Exhibition "The enchanting art of stone cutting. Morgenstern 250" Aarne Maasik’s Photos of Tartu Cathedral Estonia's National University 100: Photo exhibition “Put on Your Thinking Cap! The Hundred Faces of the University of Tartu”
12 Matti Vainio's exhibition "Findings \| Leiud" The Exhibition "The enchanting art of stone cutting. Morgenstern 250" Aarne Maasik’s Photos of Tartu Cathedral Estonia's National University 100: Photo exhibition “Put on Your Thinking Cap! The Hundred Faces of the University of Tartu”	13 Sofia Raquel Alves Oliveira “HPLC analysis of bacterial alarmone nucleotide (p)ppGpp and its toxic analogue ppApp” Birgit Viru “Snow cover dynamics and its impact on greenhouse gas fluxes in drained peatlands in Estonia” Kati Braschinsky “Epidemiology of primary headaches in Estonia and applicability of web-based solutions in headache epidemiology research” Ardi Tampuu “Neural Networks for Analyzing Biological Data” Iuliia Burdun "Improving groundwater table monitoring for Northern Hemisphere peatlands using optical and thermal satellite data" Matti Vainio's exhibition "Findings \| Leiud" The Exhibition "The enchanting art of stone cutting. Morgenstern 250" Aarne Maasik’s Photos of Tartu Cathedral Estonia's National University 100: Photo exhibition “Put on Your Thinking Cap! The Hundred Faces of the University of Tartu”	14 Matti Vainio's exhibition "Findings \| Leiud" The Exhibition "The enchanting art of stone cutting. Morgenstern 250" Aarne Maasik’s Photos of Tartu Cathedral Estonia's National University 100: Photo exhibition “Put on Your Thinking Cap! The Hundred Faces of the University of Tartu”	15 Events dedicated to the anniversary of the Faculty of Medicine 2020 Matti Vainio's exhibition "Findings \| Leiud" The Exhibition "The enchanting art of stone cutting. Morgenstern 250" Aarne Maasik’s Photos of Tartu Cathedral Estonia's National University 100: Photo exhibition “Put on Your Thinking Cap! The Hundred Faces of the University of Tartu”	16 Events dedicated to the anniversary of the Faculty of Medicine 2020 Matti Vainio's exhibition "Findings \| Leiud" The Exhibition "The enchanting art of stone cutting. Morgenstern 250" Aarne Maasik’s Photos of Tartu Cathedral Estonia's National University 100: Photo exhibition “Put on Your Thinking Cap! The Hundred Faces of the University of Tartu”	17 Matti Vainio's exhibition "Findings \| Leiud" The Exhibition "The enchanting art of stone cutting. Morgenstern 250" Aarne Maasik’s Photos of Tartu Cathedral Estonia's National University 100: Photo exhibition “Put on Your Thinking Cap! The Hundred Faces of the University of Tartu”	18 Matti Vainio's exhibition "Findings \| Leiud" The Exhibition "The enchanting art of stone cutting. Morgenstern 250" Aarne Maasik’s Photos of Tartu Cathedral Estonia's National University 100: Photo exhibition “Put on Your Thinking Cap! The Hundred Faces of the University of Tartu”
19 Matti Vainio's exhibition "Findings \| Leiud" The Exhibition "The enchanting art of stone cutting. Morgenstern 250" Aarne Maasik’s Photos of Tartu Cathedral Estonia's National University 100: Photo exhibition “Put on Your Thinking Cap! The Hundred Faces of the University of Tartu”	20 Matti Vainio's exhibition "Findings \| Leiud" The Exhibition "The enchanting art of stone cutting. Morgenstern 250" Aarne Maasik’s Photos of Tartu Cathedral Estonia's National University 100: Photo exhibition “Put on Your Thinking Cap! The Hundred Faces of the University of Tartu”	21 Matti Vainio's exhibition "Findings \| Leiud" The Exhibition "The enchanting art of stone cutting. Morgenstern 250" Aarne Maasik’s Photos of Tartu Cathedral Estonia's National University 100: Photo exhibition “Put on Your Thinking Cap! The Hundred Faces of the University of Tartu”	22 Dorpater Dozentenabend international faculty club season’s opening meeting Matti Vainio's exhibition "Findings \| Leiud" The Exhibition "The enchanting art of stone cutting. Morgenstern 250" Aarne Maasik’s Photos of Tartu Cathedral Estonia's National University 100: Photo exhibition “Put on Your Thinking Cap! The Hundred Faces of the University of Tartu”	23 Matti Vainio's exhibition "Findings \| Leiud" The Exhibition "The enchanting art of stone cutting. Morgenstern 250" Aarne Maasik’s Photos of Tartu Cathedral Estonia's National University 100: Photo exhibition “Put on Your Thinking Cap! The Hundred Faces of the University of Tartu”	24 Planetarium show (in Russian) at the Tartu Old Observatory Matti Vainio's exhibition "Findings \| Leiud" The Exhibition "The enchanting art of stone cutting. Morgenstern 250" Aarne Maasik’s Photos of Tartu Cathedral Estonia's National University 100: Photo exhibition “Put on Your Thinking Cap! The Hundred Faces of the University of Tartu”	25 Matti Vainio's exhibition "Findings \| Leiud" The Exhibition "The enchanting art of stone cutting. Morgenstern 250" Aarne Maasik’s Photos of Tartu Cathedral Estonia's National University 100: Photo exhibition “Put on Your Thinking Cap! The Hundred Faces of the University of Tartu”
26 Matti Vainio's exhibition "Findings \| Leiud" The Exhibition "The enchanting art of stone cutting. Morgenstern 250" Aarne Maasik’s Photos of Tartu Cathedral Estonia's National University 100: Photo exhibition “Put on Your Thinking Cap! The Hundred Faces of the University of Tartu”	27 Matti Vainio's exhibition "Findings \| Leiud" The Exhibition "The enchanting art of stone cutting. Morgenstern 250" Aarne Maasik’s Photos of Tartu Cathedral Estonia's National University 100: Photo exhibition “Put on Your Thinking Cap! The Hundred Faces of the University of Tartu”	28 Triinu Vihmann “Ionic liquids: synthesis and application in lubrication and lithography” Matti Vainio's exhibition "Findings \| Leiud" The Exhibition "The enchanting art of stone cutting. Morgenstern 250" Aarne Maasik’s Photos of Tartu Cathedral Estonia's National University 100: Photo exhibition “Put on Your Thinking Cap! The Hundred Faces of the University of Tartu”	29 Matti Vainio's exhibition "Findings \| Leiud" The Exhibition "The enchanting art of stone cutting. Morgenstern 250" Aarne Maasik’s Photos of Tartu Cathedral Estonia's National University 100: Photo exhibition “Put on Your Thinking Cap! The Hundred Faces of the University of Tartu”	30 Matti Vainio's exhibition "Findings \| Leiud" The Exhibition "The enchanting art of stone cutting. Morgenstern 250" Aarne Maasik’s Photos of Tartu Cathedral Estonia's National University 100: Photo exhibition “Put on Your Thinking Cap! The Hundred Faces of the University of Tartu”	31 Matti Vainio's exhibition "Findings \| Leiud" The Exhibition "The enchanting art of stone cutting. Morgenstern 250" Aarne Maasik’s Photos of Tartu Cathedral Estonia's National University 100: Photo exhibition “Put on Your Thinking Cap! The Hundred Faces of the University of Tartu”

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Erge Ideon "Rational spline collocation for boundary value problems"

October