Construction and Numerical Resolution of High-Order Accuracy Decomposition Scheme for a Quasi-Linear Evolution Equation

Abstract

In the present work the Cauchy problem for an abstract evolution equation with a Lipschitz-continuous operator is considered, where the main operator represents the sum of positive definite self-adjoint operators. The fourth-order accuracy decomposition scheme is constructed for an approximate solution of the problem. The theorem on the error estimate of an approximate solution is proved. Numerical calculations for different model problems are carried out using the constructed scheme. The obtained numerical results confirm the theoretical conclusions.

Department(s)

Electrical and Computer Engineering

Keywords and Phrases

Decomposition scheme; operator splitting; quasi-linear evolution equation

International Standard Serial Number (ISSN)

1572-9176; 1072-947X

Document Type

Article - Journal

Document Version

Final Version

File Type

text

Language(s)

English

Rights

© 2024 De Gruyter, All rights reserved.

Publication Date

01 Sep 2018

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