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.
Recommended Citation
N. Dikhaminjia et al., "Construction and Numerical Resolution of High-Order Accuracy Decomposition Scheme for a Quasi-Linear Evolution Equation," Georgian Mathematical Journal, vol. 25, no. 3, pp. 337 - 348, De Gruyter, Sep 2018.
The definitive version is available at https://doi.org/10.1515/gmj-2018-0004
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