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.
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References
Braianov, I.: Convergence of a Crank-Nicolson difference scheme for heat equation with interface in the heat flow and concentrated heat capacity. Lect. Notes Comput. Sci. 1196 (1997), 58–65.
Braianov, I.; Vulkov, L.: Finite Difference Schemes with Variable Weights for Parabolic Equations with Concentrated Capacity. Notes on Numerical Fluid Dynamics, Vieweg, 62 (1998), 208–216.
Braianov, I. A., Vulkov L. G.: Homogeneous difference schemes for the heat equation with concentrated capacity. Zh. vychisl. mat. mat. fiz. 39 (1999), 254–261 (Russian).
Eschet, J.: Quasilinear parabolic systems with dynamical boundary conditions. Communs. Partial Differential Equations 19 (1993), 1309–1364.
Jovanović, B. S., Matus, P. P., Shcheglik, V. S.: Difference schemes on nonuniform meshes for the heat equation with variable coefficients and generalizad solutions. Doklady NAN Belarusi 42, No 6 (1998), 38–44 (Russian).
Jovanović, B., Vulkov, L.: On the convergence of finite difference schemes for the heat equation with concentrated capacity. Numerishe Mathematik, in press.
Lions, J. L., Magenes, E.: Non homogeneous boundary value problems and applications. Springer-Verlag, Berlin and New York, 1972.
Lykov A. V.: Heat-masstransfer. Energiya, Moscow 1978 (Russian).
Renardy, M., Rogers, R. C.: An introduction to partial differential equations. Springer-Verlag, Berlin and New York, 1993.
Riesz, F., Sz.-Nagy, B.: Leçons d’analyse fonctionelle. Akadémiai Kiadó, Budapest 1972.
Samarskii A. A.: Theory of difference schemes. Nauka, Moscow 1989 (Russian).
Samarskii A. A., Lazarov R. D., Makarov V. L.: Difference schemes for differential equations with generalized solutions. Vysshaya shkola, Moscow 1987 (Russian).
Samarskii, A. A., Mazhukin, V. I., Malafei, D. A., Matus, P. P.: Difference schemes of high order of approximation on nonuniform in space meshes. Doklady RAN 367, No 3 (1999), 1–4 (Russian).
Vladimirov, V. S.: Equations of mathematical physics. Nauka, Moscow 1988 (Russian).
Vulkov, L.: Application of Steklov-type eigenvalues problems to convergence of difference schemes for parabolic and hyperbolic equation with dynamical boundary conditions. Lect. Notes Comput. Sci. 1196 (1997), 557–564.
Wloka, J.: Partial differential equations. Cambridge Univ. Press, Cambridge 1987.
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Jovanović, B.S., Vulkov, L.G. (2001). Operator’s Approach to the Problems with Concentrated Factors. In: Vulkov, L., Yalamov, P., Waśniewski, J. (eds) Numerical Analysis and Its Applications. NAA 2000. Lecture Notes in Computer Science, vol 1988. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45262-1_51
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DOI: https://doi.org/10.1007/3-540-45262-1_51
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