Book ChapterDOI
Operator's Approach to the Problems with Concentrated Factors
Boško S. Jovanović,Lubin G. Vulkov +1 more
- pp 439-450
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Finite-difference schemes approximating the one-dimensional initial-boundary value problems for the heat equation with concentrated capacity are derived and an abstract operator's method is developed for studying such problems.Abstract:
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 operator's method is developed for studying such problems. Convergence rate estimates consistent with the smoothness of the data are obtained.read more
Citations
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Journal ArticleDOI
On the Convergence of Difference Schemes for Hyperbolic Problems with Concentrated Data
TL;DR: For finite difference schemes approximating several one-dimensional initial-boundary value problems convergence rate estimates in special discrete energetic Sobolev's norms, compatible with the smoothness of the solutions, are obtained.
Journal ArticleDOI
Numerical approximation of an interface problem for fractional in time diffusion equation
TL;DR: An initial-boundary value problem for fractional in time diffusion equation with interface with interface is considered and its well-posedness in the corresponding Sobolev spaces is proved.
Journal ArticleDOI
Finite Difference Schemes for Partial Differential Equations with Weak Solutions and Irregular Coefficients
TL;DR: In this paper, a survey of the results concerning the convergence of difference schemes for boundary value problems with generalized solutions from the Sobolev space is presented, in particular for some problems with singular coefficients.
Book ChapterDOI
Finite difference approximation of an elliptic interface problem with variable coefficients
TL;DR: Convergence rate estimate in discrete W21 norm, compatible with the smoothness of data, is obtained in general elliptic interface problem with variable coefficients and curvilinear interface.
Journal ArticleDOI
Stability of difference schemes for parabolic equations with dynamical boundary conditions and conditions on conjugation
TL;DR: In this paper, energy norms that rely on spectral problems containing the eigenvalue in the boundary conditions or conditions on conjugation are introduced and necessary and sufficient stability conditions in these norms for weighted difference schemes are established.
References
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Book
Partial Differential Equations
TL;DR: In this paper, the authors present a theory for linear PDEs: Sobolev spaces Second-order elliptic equations Linear evolution equations, Hamilton-Jacobi equations and systems of conservation laws.
Book
Non-homogeneous boundary value problems and applications
TL;DR: In this paper, the authors consider the problem of finding solutions to elliptic boundary value problems in Spaces of Analytic Functions and of Class Mk Generalizations in the case of distributions and Ultra-Distributions.
Book
The Theory of Difference Schemes
TL;DR: The theory of difference schemes was introduced in this paper, where homogeneous difference schemes and different schemes for elliptic and time-dependent equations with constant coefficients were studied. And the theory of differenceschemes symbols was discussed.
Book
An introduction to partial differential equations
Michael Renardy,Robert C. Rogers +1 more
TL;DR: In this paper, a classification of characteristics and classification of characteristics is presented, along with a discussion of conservation laws and shocks, conservation laws, maximum principles, distribution, and function spaces.