Boško S. Jovanović

On the convergence of finite difference schemes for the heat equation with concentrated capacity

Summary. We investigate the convergence of difference schemes for the one-dimensional heat equation when the coefficient at the time derivative (heat capacity) is

On the Convergence of Difference Schemes for Hyperbolic Problems with Concentrated Data

c\left( x\right) =1+K\delta \left( x-\xi \right). K = \const > 0

Operator's Approach to the Problems with Concentrated Factors

represents the magnitude of the heat capacity concentrated at the point

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

x=\xi

Finite difference approximations of generalized solutions

. An abstract operator method is developed for analyzing this equation. Estimates for the rate of convergence in special discrete energetic Sobolevs norms, compatible with the smoothness of the solution are obtained.

Construction and Convergence of Difference Schemes for a Model Elliptic Equation with Dirac-delta Function Coefficient

Hyperbolic equations with unbounded coefficients and even generalized functions (in particular, Dirac-delta functions) occur both naturally and artificially and must be treated in numerical schemes. An abstract operator method is proposed for studying these equations. For finite difference schemes approximating several one-dimensional initial-boundary value problems convergence rate estimates in special discrete energetic Sobolevs norms, compatible with the smoothness of the solutions, are obtained.

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

In this paper finite-difference schemes approximating the one-dimensional initial-boundary value problems for the heat equation with concentrated capacity are derived. An abstract operators method is developed for studying such problems. Convergence rate estimates consistent with the smoothness of the data are obtained.

Numerical approximation of an interface problem for fractional in time diffusion equation

Abstract: 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.

Finite difference approximation of an elliptic interface problem with variable coefficients

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.

Fractional Order Convergence Rate Estimates Of Finite Difference Method On Nonuniform Meshes

We first discuss the difficulties that arise at the construction of difference schemes on uniform meshes for a specific elliptic interface problem. Estimates for the rate of convergence in discrete energetic Sobolevs norms compatible with the smoothness of the solution are also presented.