Geodesic
On a semi-variational method for parabolic equations. II
Applications of Mathematics, Tome 18 (1973) no. 1, pp. 43-64
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The invariance of the $n$-th semivariational approximation with respect to the polynomial bases and its coincidence with the $n$-th Padé approximation at the basic time instants are proved for the case of the homogeneous abstract parabolic equation. The method and theorems are also extended to parabolic problems with inhomogeneous boundary conditions and to equations with two positive definite operators.
The invariance of the $n$-th semivariational approximation with respect to the polynomial bases and its coincidence with the $n$-th Padé approximation at the basic time instants are proved for the case of the homogeneous abstract parabolic equation. The method and theorems are also extended to parabolic problems with inhomogeneous boundary conditions and to equations with two positive definite operators.
DOI : 10.21136/AM.1973.103447
Classification : 65L05, 65M10, 65M99, 65N30 
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Hlaváček, Ivan. On a semi-variational method for parabolic equations. II. Applications of Mathematics, Tome 18 (1973) no. 1, pp. 43-64. doi: 10.21136/AM.1973.103447

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[3] I. Hlaváček J. Nečas: On inequalities of Korn's type. Archive for Rational Mechanics and Analysis, 36, 4, 1970, 305-344. | DOI | MR

[4] J. Nečas: Les méthodes directes en théorie des équations elliptiques. Prague, Academia 1967. | MR

[5] J. Douglas, Jr. T. Dupont: Galerkin methods for parabolic equations. SIAM J. Numer. Anal. 7, 1970,4, 575-626. | MR

[6] R. S. Vargа: Matrix iterative Analysis. Prentice-Hall, 1962. | MR

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