AM 255 : Problem Set 4
نویسنده
چکیده
Prove that the θ scheme (I − θkD + D −)v n+1 j = (I + (1 − θ)kD + D −)v n j , j = 0, 1,. .. , N, 0 ≤ θ ≤ 1 (1) is unconditionally stable for θ ≥ 1 2. In order to find the necessary conditions for stability, we begin by making the ansatz v n j = 1 √ 2π e iωx j ˆ v n (ω), where the solution is composed of a single Fourier component. Substituting this expression into Equation 1, we obtain the following result.
منابع مشابه
SOLVING MULTI CONSTRAINTS STRUCTURAL TOPOLOGY OPTIMIZATION PROBLEM WITH REFORMULATION OF LEVEL SET METHOD
Due to the favorable performance of structural topology optimization to create a proper understanding in the early stages of design, this issue is taken into consideration from the standpoint of research or industrial application in recent decades. Over the last three decades, several methods have been proposed for topology optimization. One of the methods that has been effectively used in stru...
متن کاملDevelopment of a Genetic Algorithm for Advertising Time Allocation Problems
Commercial advertising is the main source of income for TV channels and allocation of advertising time slots for maximizing broadcasting revenues is the major problem faced by TV channel planners. In this paper, the problem of scheduling advertisements on prime-time of a TV channel is considered. The problem is formulated as a multi-unit combinatorial auction based mathematical model. This is a...
متن کاملThulstrup AM, Hannerz H, Hougaard KS: Exposure to psycho- social job strain during pregnancy and odds of asthma and atopic dermatitis among 7-year old children - a prospective
The 4 original papers are 1. Larsen AD, Hannerz H, Obel C, Thulstrup AM, Bonde JP, Hougaard KS: Testing the association between psychosocial job strain and adverse birth outcomes design and methods. BMC Public Health 2011, 11: 255. 2. Larsen AD, Hannerz H, Juhl M, Obel C, Thulstrup AM, Bonde JP, Hougaard KS: Psychosocial job strain and risk of adverse birth outcomes: a study within the Danish n...
متن کاملPlatelet antigens in varicella associated thrombocytopenia
1 Feusner JH, Slichter SJ, Harker LA. Mechanisms of thrombocytopenia in varicella. Am J Hematol 1979;7: 255-64. 2 Espinoza G, Kuhn C, Viral infection of megakaryocytes in varicella with purpura. Am J Clin Pathol 1974;61:203-8. 3 Winiarski J. IgG and IgM antibodies to platelet membrane glycoprotein antigens in acute childhood idiopathic thrombocytopenic purpura. BrJ Haematol 1989;73:88-92. 4 Win...
متن کاملAPX-hardness of domination problems in circle graphs
We show that the problem of finding a minimum dominating set in a circle graph is APXhard: there is a constant δ > 0 such that there is no (1 + δ)-approximation algorithm for the minimum dominating set problem on circle graphs unless P = NP. Hence a PTAS for this problem seems unlikely. This hardness result complements the (2 + ε)-approximation algorithm for the problem (Journal of Algorithms, ...
متن کامل