Mathematical Modelling and Numerical Analysis

The department of “Mathematical Modelling and Numerical Analysis” was created in March 2014 through the merger of the departments: “Mathematical Modelling”, “Computational Mathematics” and “Biomathematics”.

The department members work in the areas of numerical analysis, functional analysis, approximation theory, error analysis, convex and interval analysis with application in mathematical modeling of processes in geophysics, biology, chemistry, economics, medicine and engineering. The department develops effective numerical methods and algorithms for solving linear and non-linear partial differential and integral equations and systems, numerical methods with result verification, and for the study of controllability of dynamic systems.

Besides scientific research, department members teach at universities in Bulgaria and abroad. A large number of scientists have defended doctoral theses under the guidance of department members.

The department continues the tradition of the Bulgarian school of approximation theory, founded by academician Blagovest Sendov in the early 1970s. The department organises the international conference “Constructive theory of functions”, which has been held since 1971, and is a co-organiser of the international conference “Biomath”.

The department is also a co-organiser of a series of seminars on Computational Mathematics and Approximation Theory, which have been held once a year since 2012, in collaboration with Johannes Kepler University Linz, Austria.

During the past decade the department members have actively participated in scientific projects financed by various sources.

Projects financed by the Fund for Scientific Research and the Ministry of Education and Science:

  • New directions in approximation theory (КП-06-Н62/4, 2022-2025)
  • Application of analytical and numerical methods for solving nonlinear systems describing elastic structures (КП-06-Н22/2, 2018-2021)
  • National co-financing for the participation of Bulgarian collectives in established actions under the European Programme for Cooperation in the Field of Scientific Research and Technology COST for Action 16227 (ДКОСТ 01/29, 2017-2019)
  • Modern methods in the constructive theory of functions (ДН 02/14, 2016-2019)
  • Computer modeling and clinical studies of arterial aneurysms in humans (ДФНИ-И02/3, 2014-2018)
  • Theoretical and numerical study of nonlinear mathematical models (ДФНИ-И02/9, 2014-2017)
  • Algorithms for approximate recovery of functions based on Radon projections and partial differential equations (ДМУ 03/17, 2011-2017)
  • Efficient multilevel methods and algorithms for problems with heterogeneous coefficients (ДМУ 03/62, 2011-2014)
  • Numerical and analytical methods for obtaining localized solutions of generalized multidimensional wave equations (ДДВУ 02/71, 2010-2014)
  • National scientific programme “Information and communication technologies for a single digital market in science, education and security (IKTvNOS)”, (ДО1-205/23.11.2018, 2018-2020)
  • National Geoinformation Center (NGIC) for monitoring, assessment and forecasting of natural and anthropogenic risks and disasters (ДО1-161/28.08.2018, 2018-2023) within the framework of the National Roadmap for Scientific Infrastructure (2017-2023)
  • International Research Infrastructure Joint Institute for Nuclear Research, Dubna, Russia, under the National Science Infrastructure Roadmap (2017-2023)

Projects financed under EU programmes:

  • European Research and Technology Cooperation Program COST Action 16227 Investigation and Mathematical Analysis of Avant-garde Disease Control via Mosquito Nano-Tech-Repellents (2017-2021)
  • Centre for Excellence in Informatics and Information and Communication Technologies, contract BG05M2OP001-1.001-0003 under the Operational Program “Science and Education for Smart Growth” (2014-2020), co-financed by the European Union through the European Structural and Investment Funds (2018-2023)
  • MMAC: Centre of Excellence for Mathematical Modeling and Advanced Computing in Science and Engineering, European programme Horizon 2020 Spreading excellence and widening participation programme (contract #664406, 2015-2016)
  • Contracts Д03-153,154/02.04.2014, Д01-4106/17.06.2013, Д02-793/28.08.2012, financed under project BG051PO001/3.3-05-0001 “Science and Business”, OP “Human Resources” of the European Social Fund

Projects under the Bulgaria-Austria bilateral cooperation program of the Fund for Scientific Research:

  • Numerical and Symbolic Approximation with Radon Projections (with Research Institute for Symbolic Computation, Johannes Kepler University Linz, Austria, ДНТС Австрия 01/6, 2012-2018)
  • Low-rank approximations, polynomials, splines and their applications (with Institute of Computational Mathematics, Johannes Kepler University Linz, Austria)
  • Theory and algorithms for approximation with polynomials and splines (with Johann Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences, Austria, ДНТС/Австрия КП-06, 2019-2021)

National scientific programme “Petar Beron i NIE”:

  • Reduced basis methods with application in modelling tumor growth and evolution (КП-06-ДБ-5, 2020-2022)

Other international projects:

  • Mathematical modeling of nonlinear systems and physical processes (with the Joint Institute for Nuclear Research, Dubna, Russia, 2010-2019)
  • Approximation theory and Fourier analysis (with Alfréd Rényi Institute of Mathematics of the Hungarian Academy of Sciences, 2013-2015)
  • Theoretical Properties and Interval Methods for Parametric Linear Systems (with Charles University, Prague, Czech Republic, 2015-2018)
  • Parametric Linear Interval Systems (with Bergische Universität Wuppertal (DFG), Germany, 2004-2014)