Displaying similar documents to “High degree precision decomposition method for the evolution problem with an operator under a split form”

The fourth order accuracy decomposition scheme for an evolution problem

Zurab Gegechkori, Jemal Rogava, Mikheil Tsiklauri (2004)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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In the present work, the symmetrized sequential-parallel decomposition method with the fourth order accuracy for the solution of Cauchy abstract problem with an operator under a split form is presented. The fourth order accuracy is reached by introducing a complex coefficient with the positive real part. For the considered scheme, the explicit a priori estimate is obtained.

On α-times integrated C-semigroups and the abstract Cauchy problem

Chung-Cheng Kuo, Sen-Yen Shaw (2000)

Studia Mathematica

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This paper is concerned with α-times integrated C-semigroups for α > 0 and the associated abstract Cauchy problem: u ' ( t ) = A u ( t ) + t α - 1 Γ ( α ) x , t >0; u(0) = 0. We first investigate basic properties of an α-times integrated C-semigroup which may not be exponentially bounded. We then characterize the generator A of an exponentially bounded α-times integrated C-semigroup, either in terms of its Laplace transforms or in terms of existence of a unique solution of the above abstract Cauchy problem for every x...