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Information × Registration Number 0221U100567, 0118U000610 , R & D reports Title Computer modeling of complex systems. popup.stage_title Head Savula Yarema H, Доктор фізико-математичних наук Registration Date 07-01-2021 Organization Ivan Franko National University of Lviv popup.description2  In this research project we consider the actual problems of computer modelling of complex systems which behavior are modeled by linear and non-linear initial value problems and initial-boundary value problems. Research of the following problems are presented in this report: exponential substitution in the finite element method for singularly perturbed advection-diffusion-reaction problems; development of explicit and implicit scheme for the discretization in time of the nonlinear hyperbolic initial-boundary value problem; application of cellular automata and the mortar finite element method to solve two-dimensional topological optimization problems for elasticity theory models; qualitative analysis of mathematical models of fermentation processes; mathematical modeling of the cancer growth process and construction of a numerical algorithm to solve this model; construction of surrogate models (reduced-order models) for systems of ordinary differential equations and partial differential equations based on the method of orthogonal decomposition and radial basis functions. The efficiency of the proposed algorithms is confirmed by the numerical experiments and mathematical rigor of proving. Product Description popup.authors popup.nrat_date 2021-03-17 Close