Metody aplikované matematiky v inženýrských problémech
K osmdesátinám České matice technické
Die Lösung der gemischten Randwertaufgabe und des Problems mit einer Integralbedingung ``im Ganzen'' für eine nichtlineare parabolische Gleichung mit der Netzmethode
Die Lösung der ersten Randwertproblems „im Ganzen‟ für eine nichtlineare parabolische Gleichung mit der Netzmethode
On the method of least squares on the boundary
A proof of monotony of the Temple quotients in eigenvalue problems
If the so-called Collatz method is applied to get twosided estimates of the first eigenvalue , the sequences of the so-called Schwarz quatients (which are upper bounds for ) and of the so-called Temple quotients (which are lower bounds) are constructed. While monotony of the first sequence was proved many years ago, monotony of the second one has been proved only recently by F. goerisch and J. Albrecht in their common paper “Die Monotonie der Templeschen Quotienten” (ZAMM, in print). In the present...
Dvě věty o řešení rovnice
K 80. výročí narození profesora Vyčichla
Užití Lagrangeových rovnic II. druhu ke studiu činnosti jednoho strojního zařízení
On application of direct variational methods to the solution of parabolic boundary value problems of arbitrary order in the space variables
Poválečný rozvoj perspektivy aplikované matematiky
On a method of two-sided eigenvalue estimates for elliptic equations of the form
The Collatz method of twosided eigenvalue estimates was extended by K. Rektorys in his monography Variational Methods to the case of differential equations of the form with elliptic operators. This method requires to solve, successively, certain boundary value problems. In the case of partial differential equations, these problems are to be solved approximately, as a rule, and this is the source of further errors. In the work, it is shown how to estimate these additional errors, or how to avoid...
A note on nonhomogeneous initial and boundary conditions in parabolic problems solved by the Rothe method
When solving parabolic problems by the so-called Rothe method (see K. Rektorys, Czech. Math. J. 21 (96), 1971, 318-330 and other authors), some difficulties of theoretical nature are encountered in the case of nonhomogeneous initial and boundary conditions. As a rule, these difficulties lead to rather unnatural additional conditions imposed on the corresponding bilinear form and the initial and boundary functions. In the present paper, it is shown how to remove such additional assumptions in the...
Solution of the first biharmonic problem by the method of least squares on the boundary
Application of the Ritz method to the solution of parabolic boundary value problems of arbitrary order in the space variables
The method of discretization in time and partial differential equations
Numerical and theoretical treating of evolution problems by the method of discretization in time
Solution of the first problem of plane elasticity for multiply connected regions by the method of least squares on the boundary. I
Solution of the first problem of plane elasticity for multiply connected regions by the method of least squares on the boundary. II
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