Contents

Pre ac

Part I

Invited lectures

S ew-Ham ton an an Ham ton an E va ue Pro ems: T eor , A or t m n A cat ons P B Kressne olker Mehrmann 1 Pr limin ri T e S ew-Ham ton an E genva ue Pro em 3 T e Ham ton an E enva ue Pro em A cat ons Concludin Remarks c now e gments

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enera Frame or t e onstruct on o onstra ne ur es Paolo Costantini, Maria Lucia Sampol 1 In r i n T e genera structure o A stract Sc eme onstruct on o constra ne cur e A new application: eometric interpolation 5 Concludin remarks

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MBVP for Tension Splines Bor s I. Kvasov 1 In r i 1–D DMBVP. Finite Difference A roximation 3 System Sp tt ng an Mes So ut on Extens on Computational Aspect 2–D DMBVP. Problem Formulation Finite–Difference A roximation of DMBVP Al orithm 8 SOR Iterative Metho Method of Fractional Step

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10 Grap ca Examp es cknowled ments

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Robust numerical methods for the sin ularl perturbed Black-Scholes equation H Mille I hishkin 1 In r i 2 Pr l m f rm l i Numer ca so ut ons o s ngu ar pertur at on pro em 4 Upwind uniform mesh method 5 Upwind piecewise-uniform ﬁtted mesh method Summary Ac now e gment

eference

Part II

Contributed lectures

On certa n propert es o spaces o oca y So o ev unct on ena Antoni´ Kr m Buraz 1 Intro uct on 2 Spaces of locall Sobolev function , , Dua ty o spaceΩnΩ Weak convergence and some imbedding Concluding remark

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TIN

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n some properties of homogenised coefﬁcients for stationary diffusion problem 121 ena Antoni´ Mar o Vr o ja 1 Intro uct on 12 T o- mens ona case T ree- mens ona cas 12 Some spec a case

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So v n Para o c S n u ar Pertur e Pro Splines Beroˇ o Maruˇ In r n o ocat on met o 3 Co ocat on met o or ara o c 4 Numer ca resu t

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On accurac propert es o one–s e a ona zat on a or t m an i n Bosne o Drmaˇ 1 In r i One–s e a ona zat on 3 Error anal si On the (i)relevance of the (non)orthogonality of onclusion

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Knot Insertion Al orithms for Wei hted Spline na Bosner 1 In r i n n Pr limin ri Weighted splines of order 4 3 We te sp nes o or er+ Conclusion

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ts app ca-

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umer ca proce ures or t e eterm nat on o an un nown source parameter n arabolic e uation 16 Emine an Baran 1 In r i 61 Proce ure I (canon ca representat on) 1 2 3 Procedure II (TTF formulation 16 Numer ca Resu t an D scuss on 1 4

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Balanced central NT schemes for the shallow water e uations e i a rnjari´ c Sen Vu ovi´ u a Sopta 1 Central NT scheme Balanced central NT scheme for the shallow water e uations. 3 Numerical results onc us on remar s

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H en Mar ov Mo e s an Mu t p e A Pa tei Karag te o 1 Intro uct on Hidden Markov Model 3 Expectat on Max m zat on 4 Suboptimal Ali nment Results and Conclusion

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nments o Prote n Sequences 187 I ana Ni ´ Mari Tadi´ omago Vlah 1 188 189

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Tota east squares pro em or t e Hu ert unct on Dra Juki´ Rudol Scitovski ristian ab 1 In r i n The existence roblem and its solution 3 C o ce o n t a a rox mat on Numer ca exam e

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APPLIED MATHEMATI

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ne- mens ona ow o a com ress e v scous m cro o ar e so ut on Nermina Mu akovi´ 1 Statement of the roblem and the main result Some properties of the nonstationar solution 3 Proof of Theorem 1.1.

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eometric Interpolation of Data i erne Koza Em Za ar 1 In r i n The s stem of nonlinear equation 3 The roof of the theorem Numerical exam le

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Heat n o o we ot water c rcu at o M a Jura r o Prni´ 1 M m m Var at ona ro e 3 Numer ca a rox mat on

n the dimension of bivariate spline space 3 aˇ Ja ˇ Jernej Koza 1 Intro uct on T e a roac es to t e mens on ro 3 T e re uct on step T e re uct on poss t es cons ere

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n stron cons stenc or one–step approx mat ons o stoc ast c or ential equations Horv Bo or 1 Intro uct on Stron Conver ence an Cons stenc

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On parameter classes of solutions for system of quasilinear differential equations 2 3 A Omerspa B ˇ Vr o Intro uct o Th m in r l 26

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A ge ra c Proo o t e B–Sp ne Der vat ve Formu a en Rogin Intro uct on an pre m nar e T e er at e ormu a Acknowledgment

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Re at ve Pertur at ons, Ran Sta t an Zero Patterns o Matr ce San a Singe a Sin e 1 Intro uct on 2 Problem reduction for rank deﬁcient matrice 3 Vanishin determinant stabilit 4 Zero patterns

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umer ca S mu at ons o Water Wave Propa at on an F oo ˇ ˇ uka Sopt Nelida Crn ari´-Z u o ´ Dan o Ho

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Intro uct on Wetting and drying mu at on

Der vat on o a mo e o ea spr n s osi Tambaˇ 1 Intro uct on 2 Geometry of straight multileaf springs 3D e ast c t pro em 4 T e pro em n epen ent oma 5 A riori estimate The ﬁrst test function Th n f n i n T e mo e

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uantum s te perco at on on amena e rap

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erko S

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Ivan Vese 1

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Introduction: The Quantum ercolation mode Results: Spectral properties of ﬁnite range hopping operators Proo s o t e t eorems Outlook: ﬁnitel supported and exponentiall deca in states

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rder of Accuracy of Extended WENO Schemes enk Neli r Z Sop 1 Intro uct on 2 Extended WENO scheme 3 Application to one-dimensional shallow water equations App cat on to one- mens ona near acoust cs equat ons Application to one-dimensional Bur ers equations with source ter escr n at metr 6 Concluding remark

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