Bosko Jovanovic - Academia.edu (original) (raw)

Papers by Bosko Jovanovic

Research paper thumbnail of Quantitative Methods of Analysis of Footprinting Diagrams for the Complexes Formed by a Ligand with a DNA Fragment of Known Sequence

Annals of the New York Academy of Sciences, 2005

The regulation of gene expression is based on the interaction of DNA with different ligands. A mo... more The regulation of gene expression is based on the interaction of DNA with different ligands. A model of adsorption was considered that can be applied to the quantitative analysis of footprinting diagrams for the complexes formed by a ligand with a DNA fragment of known structure. This model allows the probabilities of ligand binding to DNA sites with a known sequence to be calculated and the variance of probabilities of ligand binding with a specified binding site to be estimated. The model was used for quantitative analysis of diagrams of DNAse footprinting for the complexes of the dimeric analogue of the antitumor antibiotic netropsin. Experimental and theoretically calculated profiles of distribution of netropsin bound on DNA are in good agreement with one another.

Research paper thumbnail of Micropolar fluid between two coaxial cylinders (numerical approach)

Theoretical and Applied Mechanics, 2021

The paper describes the flow of a suspension which is a mixture of two phases: liquid and solid g... more The paper describes the flow of a suspension which is a mixture of two phases: liquid and solid granules. The continuum model with microstructure is introduced, which involves two independent kinematic quantities: the velocity vector and the micro-rotation vector. The physical analogy is based on the movement of the suspension between two coaxial cylinders. The inner cylinder is stationary and the outer one rotates with constant angular velocity. This physical analogy enabled a mathematical model in a form of two coupled differential equations with variable coefficients. The aim of the paper is to present the numerical aspect of the solution for this complex mathematical model. It is assumed that the solid granules are identically oriented and that under the influence of the fluid they move translationally or rotate around the symmetry axis but the direction of their symmetry axes does not change. The solution was obtained by the ordinary finite difference method, and then the corre...

Research paper thumbnail of Convergence of a Factorized Finite Difference Scheme for a Parabolic Transmission Problem

In this paper, we consider a non-standard parabolic transmission problem in disjoint domains. A p... more In this paper, we consider a non-standard parabolic transmission problem in disjoint domains. A priori estimate for its weak solution in appropriate Sobolev-like space is proved. The convergence of a factorized finite difference scheme approximating this problem is analyzed.

Research paper thumbnail of Finite Difference Schemes for Partial Differential Equations with Weak Solutions and Irregular Coefficients

Computational Methods in Applied Mathematics, 2004

A survey of the results concerning the convergence of finite difference schemes for boundary value... more A survey of the results concerning the convergence of finite difference schemes for boundary value problems with generalized solutions from the Sobolev space is presented. In particular, difference schemes for some problems with singular coefficients are investigated.

Research paper thumbnail of Additive difference scheme for two-dimensional fractional in time diffusion equation

Filomat, 2017

An additive finite-difference scheme for numerical approximation of initial-boundary value proble... more An additive finite-difference scheme for numerical approximation of initial-boundary value problem for two-dimensional fractional in time diffusion equation is proposed. Its stability is investigated and a convergence rate estimate is obtained.

Research paper thumbnail of Application of the Two-grid Method to a Heat Radiation Problem

AIP Conference Proceedings, 2009

We consider a nonlinear elliptic boundary value problem, which describes a radiative heat transfe... more We consider a nonlinear elliptic boundary value problem, which describes a radiative heat transfer. This paper is concerned with the solution of the nonlinear system of equations arising from FEM approximations of the problem. We employ Newton’s method to develop a new version of the two‐grid method originated from O. Axelson and J. Xu. Numerical results are given to a simple problem with exact solution and to a simplified version of the physical problem.

Research paper thumbnail of Factorized difference scheme for two-dimensional subdiffusion equation in nonhomogeneous media

Publications de l'Institut Mathematique, 2016

A factorized finite-difference scheme for numerical approximation of initial-boundary value probl... more A factorized finite-difference scheme for numerical approximation of initial-boundary value problem for two-dimensional subdiffusion equation in nonhomogeneous media is proposed. Its stability and convergence are investigated. The corresponding error bounds are obtained.

Research paper thumbnail of Finite difference approximation of an elliptic problem with nonlocal boundary condition

Research paper thumbnail of An iterative vector method for solving elliptic difference problems

Research paper thumbnail of Finite Difference Method for the Heat Equation with Coefficient from Anisotropic Sobolev Space

In this paper we consider the first initial-boundary value problem for the heat equation with var... more In this paper we consider the first initial-boundary value problem for the heat equation with variable coeficient in a domain (0, 1) × (0, T ]. We assume that the solution of the problem and the coefficient of equation belong to the corresponding anisotropic Sobolev spaces. Convergence rate estimate which is consistent with the smoothness of the data is obtained.

Research paper thumbnail of Interpolation technique and convergence rate estimates for finite difference method

Lecture Notes in Computer Science, 1997

In this work we expose a methodology for establishing convergence rate estimates for finite diffe... more In this work we expose a methodology for establishing convergence rate estimates for finite difference schemes based on the interpolation theory of Banach spaces. As a model problem we consider Dirichlet boundary value problem for second order linear elliptic equation with variable coefficients from Sobolev spaces. Using interpolation theory we construct fractional-order convergence rate estimates which are consistent with the smoothness of data.

Research paper thumbnail of Finite Difference Approximation of an Elliptic Interface Problem with Variable Coefficients

Lecture Notes in Computer Science, 2005

... where ξ = (ξ1,ξ2), MU = − 2 ∑ i,j=1 Aij(ξ) ∂2U ∂ξi∂ξj + 2 2 ∑ i=1 Bi(ξ) ∂U ∂ξi + C(ξ)U , Aij(... more ... where ξ = (ξ1,ξ2), MU = − 2 ∑ i,j=1 Aij(ξ) ∂2U ∂ξi∂ξj + 2 2 ∑ i=1 Bi(ξ) ∂U ∂ξi + C(ξ)U , Aij(ξ) = Aji(ξ) is elliptic operator and δS(ξ) is Dirac distribution concentrated on S. The equal-ity in (1) is treated in the sense of distributions. ... 2 ∑ i=1 [ bi ∂u ∂xi + ∂(biu) ∂xi ] + cu , (4) ...

Research paper thumbnail of Finite Element Approximation of an Elliptic Boundary Value Problem with Interface

Lecture Notes in Computer Science, 2009

For elliptic boundary value problem in domain with smooth curvilinear boundary and interface a fi... more For elliptic boundary value problem in domain with smooth curvilinear boundary and interface a finite element approximation is constructed. Convergence is proved in Sobolev like spaces W 1 2 and L2.

Research paper thumbnail of On the Numerical Solution of a Transmission Eigenvalue Problem

Lecture Notes in Computer Science, 2009

A transmission eigenvalue problem in disjoint intervals is examined. Distribution of the eigenval... more A transmission eigenvalue problem in disjoint intervals is examined. Distribution of the eigenvalues is obtained. The corresponding difference scheme is proposed and tested on few numerical examples.

Research paper thumbnail of Numerical Analysis of Blow-Up Weak Solutions to Semilinear Hyperbolic Equations

Lecture Notes in Computer Science

We study numerical approximations of weak solutions of hyperbolic problems with discontinuous coe... more We study numerical approximations of weak solutions of hyperbolic problems with discontinuous coefficients and nonlinear source terms in the equation. By a semidiscretization of a Dirichlet problem in the space variable we obtain a system of ordinary differential equations (SODEs), which is expected to be an approximation of the original problem. We show at conditions similar to those for the hyperbolic problem, that the solution of the SODEs blows up. Under certain assumptions, we also prove that the numerical blow-up time converges to the real blow-up time when the mesh size goes to zero. Numerical experiments are analyzed.

Research paper thumbnail of On the strong stability of differential equations and difference schemes

PAMM, 2005

Paper deals with the construction of a priori estimates for the solution of Cauchy problem for an... more Paper deals with the construction of a priori estimates for the solution of Cauchy problem for an abstract linear differential equation in Hilbert space under perturbations of the initial condition, right‐hand side, and operators of the problem. It is shown that a priori estimates of strong stability can be obtained directly on the basis of various a priori estimates for the solution of the Cauchy problem. The perturbations of the operators of the problem are estimated in the corresponding operator norms. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Research paper thumbnail of Finite Difference Approximations of Generalized Solutions

Mathematics of Computation, 1985

We consider finite difference schemes approximating the Dirichlet problem for the Poisson equatio... more We consider finite difference schemes approximating the Dirichlet problem for the Poisson equation. We provide scales of error estimates in discrete Sobolev-like norms assuming that the generalized solution belongs to a nonnegative order Sobolev space.

Research paper thumbnail of Finite Difference Approximation of a Hyperbolic Transmission Problem

Springer Optimization and Its Applications, 2010

In this paper we investigate an initial boundary value problem for a one-dimensional hyperbolic e... more In this paper we investigate an initial boundary value problem for a one-dimensional hyperbolic equation in two disjoint intervals. A finite difference scheme approximating this initial boundary value problem is proposed and analyzed. An estimate of the convergence rate is obtained.

Research paper thumbnail of About some types of boundary value problems with interfaces

Krag. J. Math, 2007

We report results concerning different types of boundary value problems with interfaces. A broad ... more We report results concerning different types of boundary value problems with interfaces. A broad class of such problems is defined. The corresponding abstract problems are investigated and some a priori estimates are presented. Intrinsic function spaces containing solutions of considered problems are introduced.

Research paper thumbnail of On the convergence of finite-difference schemes for parabolic equations with variable coefficients

Numerische Mathematik, 1989

SummaryWe study the convergence of the finite-difference schemes for the first initial-boundary v... more SummaryWe study the convergence of the finite-difference schemes for the first initial-boundary value problem for linear second-order parabolic equations with variable coefficients. Using the bilinear version of the Bramble-Hilbert lemma we obtain estimate of convergence, in discreteW21, 1/2 norm, compatible with the smoothness of generalized solutionu∈W2λ, λ/2 (Q) (1

Research paper thumbnail of Quantitative Methods of Analysis of Footprinting Diagrams for the Complexes Formed by a Ligand with a DNA Fragment of Known Sequence

Annals of the New York Academy of Sciences, 2005

The regulation of gene expression is based on the interaction of DNA with different ligands. A mo... more The regulation of gene expression is based on the interaction of DNA with different ligands. A model of adsorption was considered that can be applied to the quantitative analysis of footprinting diagrams for the complexes formed by a ligand with a DNA fragment of known structure. This model allows the probabilities of ligand binding to DNA sites with a known sequence to be calculated and the variance of probabilities of ligand binding with a specified binding site to be estimated. The model was used for quantitative analysis of diagrams of DNAse footprinting for the complexes of the dimeric analogue of the antitumor antibiotic netropsin. Experimental and theoretically calculated profiles of distribution of netropsin bound on DNA are in good agreement with one another.

Research paper thumbnail of Micropolar fluid between two coaxial cylinders (numerical approach)

Theoretical and Applied Mechanics, 2021

The paper describes the flow of a suspension which is a mixture of two phases: liquid and solid g... more The paper describes the flow of a suspension which is a mixture of two phases: liquid and solid granules. The continuum model with microstructure is introduced, which involves two independent kinematic quantities: the velocity vector and the micro-rotation vector. The physical analogy is based on the movement of the suspension between two coaxial cylinders. The inner cylinder is stationary and the outer one rotates with constant angular velocity. This physical analogy enabled a mathematical model in a form of two coupled differential equations with variable coefficients. The aim of the paper is to present the numerical aspect of the solution for this complex mathematical model. It is assumed that the solid granules are identically oriented and that under the influence of the fluid they move translationally or rotate around the symmetry axis but the direction of their symmetry axes does not change. The solution was obtained by the ordinary finite difference method, and then the corre...

Research paper thumbnail of Convergence of a Factorized Finite Difference Scheme for a Parabolic Transmission Problem

In this paper, we consider a non-standard parabolic transmission problem in disjoint domains. A p... more In this paper, we consider a non-standard parabolic transmission problem in disjoint domains. A priori estimate for its weak solution in appropriate Sobolev-like space is proved. The convergence of a factorized finite difference scheme approximating this problem is analyzed.

Research paper thumbnail of Finite Difference Schemes for Partial Differential Equations with Weak Solutions and Irregular Coefficients

Computational Methods in Applied Mathematics, 2004

A survey of the results concerning the convergence of finite difference schemes for boundary value... more A survey of the results concerning the convergence of finite difference schemes for boundary value problems with generalized solutions from the Sobolev space is presented. In particular, difference schemes for some problems with singular coefficients are investigated.

Research paper thumbnail of Additive difference scheme for two-dimensional fractional in time diffusion equation

Filomat, 2017

An additive finite-difference scheme for numerical approximation of initial-boundary value proble... more An additive finite-difference scheme for numerical approximation of initial-boundary value problem for two-dimensional fractional in time diffusion equation is proposed. Its stability is investigated and a convergence rate estimate is obtained.

Research paper thumbnail of Application of the Two-grid Method to a Heat Radiation Problem

AIP Conference Proceedings, 2009

We consider a nonlinear elliptic boundary value problem, which describes a radiative heat transfe... more We consider a nonlinear elliptic boundary value problem, which describes a radiative heat transfer. This paper is concerned with the solution of the nonlinear system of equations arising from FEM approximations of the problem. We employ Newton’s method to develop a new version of the two‐grid method originated from O. Axelson and J. Xu. Numerical results are given to a simple problem with exact solution and to a simplified version of the physical problem.

Research paper thumbnail of Factorized difference scheme for two-dimensional subdiffusion equation in nonhomogeneous media

Publications de l'Institut Mathematique, 2016

A factorized finite-difference scheme for numerical approximation of initial-boundary value probl... more A factorized finite-difference scheme for numerical approximation of initial-boundary value problem for two-dimensional subdiffusion equation in nonhomogeneous media is proposed. Its stability and convergence are investigated. The corresponding error bounds are obtained.

Research paper thumbnail of Finite difference approximation of an elliptic problem with nonlocal boundary condition

Research paper thumbnail of An iterative vector method for solving elliptic difference problems

Research paper thumbnail of Finite Difference Method for the Heat Equation with Coefficient from Anisotropic Sobolev Space

In this paper we consider the first initial-boundary value problem for the heat equation with var... more In this paper we consider the first initial-boundary value problem for the heat equation with variable coeficient in a domain (0, 1) × (0, T ]. We assume that the solution of the problem and the coefficient of equation belong to the corresponding anisotropic Sobolev spaces. Convergence rate estimate which is consistent with the smoothness of the data is obtained.

Research paper thumbnail of Interpolation technique and convergence rate estimates for finite difference method

Lecture Notes in Computer Science, 1997

In this work we expose a methodology for establishing convergence rate estimates for finite diffe... more In this work we expose a methodology for establishing convergence rate estimates for finite difference schemes based on the interpolation theory of Banach spaces. As a model problem we consider Dirichlet boundary value problem for second order linear elliptic equation with variable coefficients from Sobolev spaces. Using interpolation theory we construct fractional-order convergence rate estimates which are consistent with the smoothness of data.

Research paper thumbnail of Finite Difference Approximation of an Elliptic Interface Problem with Variable Coefficients

Lecture Notes in Computer Science, 2005

... where ξ = (ξ1,ξ2), MU = − 2 ∑ i,j=1 Aij(ξ) ∂2U ∂ξi∂ξj + 2 2 ∑ i=1 Bi(ξ) ∂U ∂ξi + C(ξ)U , Aij(... more ... where ξ = (ξ1,ξ2), MU = − 2 ∑ i,j=1 Aij(ξ) ∂2U ∂ξi∂ξj + 2 2 ∑ i=1 Bi(ξ) ∂U ∂ξi + C(ξ)U , Aij(ξ) = Aji(ξ) is elliptic operator and δS(ξ) is Dirac distribution concentrated on S. The equal-ity in (1) is treated in the sense of distributions. ... 2 ∑ i=1 [ bi ∂u ∂xi + ∂(biu) ∂xi ] + cu , (4) ...

Research paper thumbnail of Finite Element Approximation of an Elliptic Boundary Value Problem with Interface

Lecture Notes in Computer Science, 2009

For elliptic boundary value problem in domain with smooth curvilinear boundary and interface a fi... more For elliptic boundary value problem in domain with smooth curvilinear boundary and interface a finite element approximation is constructed. Convergence is proved in Sobolev like spaces W 1 2 and L2.

Research paper thumbnail of On the Numerical Solution of a Transmission Eigenvalue Problem

Lecture Notes in Computer Science, 2009

A transmission eigenvalue problem in disjoint intervals is examined. Distribution of the eigenval... more A transmission eigenvalue problem in disjoint intervals is examined. Distribution of the eigenvalues is obtained. The corresponding difference scheme is proposed and tested on few numerical examples.

Research paper thumbnail of Numerical Analysis of Blow-Up Weak Solutions to Semilinear Hyperbolic Equations

Lecture Notes in Computer Science

We study numerical approximations of weak solutions of hyperbolic problems with discontinuous coe... more We study numerical approximations of weak solutions of hyperbolic problems with discontinuous coefficients and nonlinear source terms in the equation. By a semidiscretization of a Dirichlet problem in the space variable we obtain a system of ordinary differential equations (SODEs), which is expected to be an approximation of the original problem. We show at conditions similar to those for the hyperbolic problem, that the solution of the SODEs blows up. Under certain assumptions, we also prove that the numerical blow-up time converges to the real blow-up time when the mesh size goes to zero. Numerical experiments are analyzed.

Research paper thumbnail of On the strong stability of differential equations and difference schemes

PAMM, 2005

Paper deals with the construction of a priori estimates for the solution of Cauchy problem for an... more Paper deals with the construction of a priori estimates for the solution of Cauchy problem for an abstract linear differential equation in Hilbert space under perturbations of the initial condition, right‐hand side, and operators of the problem. It is shown that a priori estimates of strong stability can be obtained directly on the basis of various a priori estimates for the solution of the Cauchy problem. The perturbations of the operators of the problem are estimated in the corresponding operator norms. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Research paper thumbnail of Finite Difference Approximations of Generalized Solutions

Mathematics of Computation, 1985

We consider finite difference schemes approximating the Dirichlet problem for the Poisson equatio... more We consider finite difference schemes approximating the Dirichlet problem for the Poisson equation. We provide scales of error estimates in discrete Sobolev-like norms assuming that the generalized solution belongs to a nonnegative order Sobolev space.

Research paper thumbnail of Finite Difference Approximation of a Hyperbolic Transmission Problem

Springer Optimization and Its Applications, 2010

In this paper we investigate an initial boundary value problem for a one-dimensional hyperbolic e... more In this paper we investigate an initial boundary value problem for a one-dimensional hyperbolic equation in two disjoint intervals. A finite difference scheme approximating this initial boundary value problem is proposed and analyzed. An estimate of the convergence rate is obtained.

Research paper thumbnail of About some types of boundary value problems with interfaces

Krag. J. Math, 2007

We report results concerning different types of boundary value problems with interfaces. A broad ... more We report results concerning different types of boundary value problems with interfaces. A broad class of such problems is defined. The corresponding abstract problems are investigated and some a priori estimates are presented. Intrinsic function spaces containing solutions of considered problems are introduced.

Research paper thumbnail of On the convergence of finite-difference schemes for parabolic equations with variable coefficients

Numerische Mathematik, 1989

SummaryWe study the convergence of the finite-difference schemes for the first initial-boundary v... more SummaryWe study the convergence of the finite-difference schemes for the first initial-boundary value problem for linear second-order parabolic equations with variable coefficients. Using the bilinear version of the Bramble-Hilbert lemma we obtain estimate of convergence, in discreteW21, 1/2 norm, compatible with the smoothness of generalized solutionu∈W2λ, λ/2 (Q) (1