on the results of Gustaf Söderlind and his groups
The Hungarian Academy of Sciences invited Professor Gustaf Söderlind to spend 6 months at our research group. During his visit in Budapest he worked in 4 topics together with our colleagues. On their new results we organized a miniworkhop with the following talks:| Gustaf Söderlind: | Convergence of linear multistep methods on smooth nonuniform grids |
| Yiannis Hadjimichael: | Local error estimation and step size control in adaptive linear multistep methods |
| Miklós Emil Mincsovics: | Consistency, stability and convergence on nonuniform grids in elliptic BVPs |
| András Molnár: | Runge-Kutta-Möbius methods |
Seminar on Applied Analysis
We continue the series of lectures on far-reaching applications of numerical analysis and modelling in the framework of the Miklós Farkas Seminar on Applied Analysis. The talks are listed on the seminar's website.Seminar on Applied Analysis
We continue the series of lectures on far-reaching applications of numerical analysis and modelling in the framework of the Miklós Farkas Seminar on Applied Analysis. The talks are listed on the seminar's website.Seminar on Applied Analysis
The joint seminar of the Departments of Analysis and Differential Equations at Budapest University of Technology and Economics was launched in September 2016 with the support of the MTA-ELTE research group Numerical Analysis and Large Networks. The founder of the seminar is professor István Faragó (Department of Differential Equations). The goal of the seminar is to help the formation of a research team working on the field of applied analysis (functional analysis, differential equations, numerical methods). The seminar tries to provide a forum for mathematicians involved in applied analysis and for researers who apply analysis. With the seminar, we would like to involve students (MSc, PhD) into our research work. See also the homepage of the seminar.| 21.09.2017 | Faragó, István: | Qualitatively reliable numerical models of time-dependent problems |
| 28.09.2017 | Kalmár-Nagy, Tamás: | Devilish eigenvalues: hysteresis and mechanistic turbulence |
| 05.10.2017 | Zachár, András: | An explicit analytic solution of a coupled first order partial and ordinary differential equation system for a discontinuous initial-boundary value problem |
| 12.10.2017 | Fekete, Imre: | On the zero-stability of multistep methods on smooth nonuniform grids |
| 19.10.2017 | Horváth, Miklós: | Inverse scattering: Mathematical properties of the phase shifts |
| 26.10.2017 | Polner, Mónika: | A space-time finite element method for neural field equations with transmission delays |
| 09.11.2017 | Mincsovics, Miklós: | What is the difference between weakly and strongly stable linear multistep methods? |
| 23.11.2017 | Lubin G. Vulkov: | Adequate numerical methods for nonlinear parabolic problems in mathematical finance |
| 30.11.2017 | Yiannis Hadjimichael: | Optimal strong stability preserving time-stepping methods with upwind- and downwind-biased operators |
| 07.12.2017 | Research reports of PhD students |
Seminar on Applied Analysis
The joint seminar of the Departments of Analysis and Differential Equations at Budapest University of Technology and Economics was launched in September 2016 with the support of the MTA-ELTE research group Numerical Analysis and Large Networks. The founder of the seminar is professor István Faragó (Department of Differential Equations). The goal of the seminar is to help the formation of a research team working on the field of applied analysis (functional analysis, differential equations, numerical methods). The seminar tries to provide a forum for mathematicians involved in applied analysis and for researers who apply analysis. With the seminar, we would like to involve students (MSc, PhD) into our research work. See also the homepage of the seminar.| 20.09.2016 | Gustaf Söderlind: | The Mathematics of Stiffness. History and Evolution of a Concept |
| 29.09.2016 | Horváth, Róbert: | Qualitative properties of numerical solutions of PDE models of disease propagation |
| 13.10.2016 | Karátson, János: | Equivalent operator preconditioning for elliptic problems |
| 20.10.2016 | Ladics, Tamás: | Error analysis of waveform relaxation method for reaction-diffusion equations |
| 27.10.2016 | Izsák, Ferenc: | Space-fractional diffusion problems: modeling and numerical solution |
| 10.11.2016 | Kovács, Balázs: | Numerical analysis of parabolic problems with dynamic boundary conditions |
| 24.11.2016 | Havasi, Ágnes: | Richardson extrapolation and its applications in environmental models |
| 01.12.2016 | Garay, Barnabás: | Metastability of a periodic orbit |
| 23.02.2017 | Gáspár Csaba: | Meshfree solutions of elliptic partial differential equations with the method of fundemental solutions |
| 02.03.2017 | Sipos András Árpád: | Uniqueness of steady state, smooth shapes in a nonlocal geometric PDE and a model for the shape evolution of ooids |
| 09.03.2017 | Snorre Christiansen: | Gaussian curvature of piecewise flat manifolds |
| 16.03.2017 | Zsuppán, Sándor: | Stokes problem, related inequalities, constants and representations |
| 30.03.2017 | Kiss, Márton: | A Chaotic Linear Operator |
| 06.04.2017 | Liepa Bikulciene: | Operator method in the theory of differential equations |
| 20.04.2017 | Csomós, Petra: | Innovative Integrators |
| 25.04.2017 | Tim Healey: | Global symmetry-breaking bifurcation in a model for 2-phase lipid-bilayer vesicles - analysis and computation |
| 05.04.2017 | Owe Axelsson: | A survey of applications of a preconditioned iterative solution method in optimal control problems, constrained by PDEs |
| 31.07.2017 | Marsha Berger: | Modeling and Simulation of Asteroid-Generated Tsunamis |
| 31.07.2017 | Randall J. LeVeque: | Adjoint Error Estimation for Adaptive Refinement of Hyperbolic PDEs |
Selected chapters from mathematical modelling of epidemic and population systems
The lectures mainly based on the textbooks V. Capasso: Mathematical Structures of Epidemic Systems, F. Brauer and Carlos Castillo-Chavez: Mathematical Models in Population Biology and Epidemiology, moreover on some selected papers dealing with the analysis of epidemic models on networks.| 30.09.2015 | Róbert Horváth: | Analysis of linear models, part I |
| 07.10.2015 | Róbert Horváth: | Analysis of linear models, part II |
| 14.10.2015 | Bálint Takács: | Spatial effects and Turing instabilities in the invasive species model |
| 11.11.2015 | Zénó Farkas: | Space-dependent population models |
| 25.11.2015 | Gabriella Sebestyén: | Modelling the population's temporal and spatial changes by partial differential equations with cross-diffusion |
Selected chapters from the theory of numerical stability
Stability is a concept that appears in various fields of mathematics, first of all in numerical mathematics. Although in each subfield stability is defined differently, there is a common meaning for this term, roughly described by the fact that perturbations are not amplifying the result in a dangerous way. The aim of the seminar is to facilitate a better understanding of this concept and discuss it within a unified framework, relying heavily on the tools of analysis and functional analysis. The lectures are at times based on the lectures of W. Hackbusch held in 2003 at the University of Kiel (Wolfgang Hackbusch: The Concept of Stability in Numerical Mathematics).Networks and differential equations
Lecturers: Fanni Sélley, András Bátkai, Dávid Kunszenti-Kovács, Péter Simon, András Szabó-Solticzky, Ádám Besenyei, Eszter Sikolya, Roxána Varga, Attila Gábor Deák Tamás Peregi, Gyula Y. Katona, Tamás Titkos, Ágnes Havasi, Ágnes Bodó, Róbert Horváth, Noémi Nagy