Displaying similar documents to “High-degree precision decomposition method for an evolution problem.”

High degree precision decomposition method for the evolution problem with an operator under a split form

Zurab Gegechkori, Jemal Rogava, Mikheil Tsiklauri (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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In the present work the symmetrized sequential-parallel decomposition method of the third degree precision for the solution of Cauchy abstract problem with an operator under a split form, is presented. The third degree precision is reached by introducing a complex coefficient with the positive real part. For the considered schema the explicit estimation is obtained.

The fourth order accuracy decomposition scheme for an evolution problem

Zurab Gegechkori, Jemal Rogava, Mikheil Tsiklauri (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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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 estimate is obtained.

High degree precision decomposition method for the evolution problem with an operator under a split form

Zurab Gegechkori, Jemal Rogava, Mikheil Tsiklauri (2002)

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

Similarity:

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

Complementarity - the way towards guaranteed error estimates

Vejchodský, Tomáš

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This paper presents a review of the complementary technique with the emphasis on computable and guaranteed upper bounds of the approximation error. For simplicity, the approach is described on a numerical solution of the Poisson problem. We derive the complementary error bounds, prove their fundamental properties, present the method of hypercircle, mention possible generalizations and show a couple of numerical examples.