Some new methods for numerical solution of initial value problems
-stabilní metody libovolně vysokého řádu
Metoda přesunu okrajových podmínek
Periodické distribuce a diskrétní Fourierova transformace
Approximate solution of an inhomogeneous abstract differential equation
Recently, we have developed the necessary and sufficient conditions under which a rational function approximates the semigroup of operators generated by an infinitesimal operator . The present paper extends these results to an inhomogeneous equation .
Transfer of boundary conditions for difference equations
It is well-known that the idea of transferring boundary conditions offers a universal and, in addition, elementary means how to investigate almost all methods for solving boundary value problems for ordinary differential equations. The aim of this paper is to show that the same approach works also for discrete problems, i.e., for difference equations. Moreover, it will be found out that some results of this kind may be obtained also for some particular two-dimensional problems.
Seventy fifth birthday of Prof. Karel Rektorys
Approximate solutions of abstract differential equations
The methods of arbitrarily high orders of accuracy for the solution of an abstract ordinary differential equation are studied. The right-hand side of the differential equation under investigation contains an unbounded operator which is an infinitesimal generator of a strongly continuous semigroup of operators. Necessary and sufficient conditions are found for a rational function to approximate the given semigroup with high accuracy.
Stability of numerical processes
Numerical stability in solution of ordinary differential equations
Über die quasistationäre Lösung der Wärmeleitungsgleichung
Vliv formulace okrajových podmínek na rychlost konvergence při řešení parciálních diferenciálních rovnic metodou sítí
Numerische Behandlung von der quasistationären Lösung der Wärmeleitungsgleichung
Matematický ústav Akademie věd padesátiletý
Transfer of boundary conditions for Poisson's equation on a circle
The method of transfer of boundary conditions yields a universal frame into which most methods for solving boundary value problems for ordinary differential equations can be included. The purpose of this paper is to show a possibility to extend the idea of transfer of conditions to a particular twodimensional problem.
Spolehlivost numerických výpočtů
Overimplicit methods for the solution of evolution problems
Transfer of conditions for singular boundary value problems
Numerical solution of linear boundary value problems for ordinary differential equations by the method of transfer of conditions consists in replacing the problem under consideration by a sequence of initial value problems. The method of transfer for systems of equations of the first order with Lebesque integrable coefficients was studied by one of the authors before. The purpose of this paper is to extend the idea of the transfer of conditions to singular boundary value problems for a linear second-order...
Overimplicit multistep methods
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