Compact finite difference schemes with high resolution characteristics and their applications to solve Burgers equation

In this article, non-standard compact finite difference schemes are constructed for the numerical approximation to first- and second-order derivatives. The proposed compact schemes have eighth order of accuracy and are tri-diagonal in nature, making use of a stencil smaller than those of conventiona...

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Bibliographic Details
Published inComputational & applied mathematics Vol. 43; no. 3
Main Authors Ramos, Higinio, Mehta, Akansha, Singh, Gurjinder
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.04.2024
Springer Nature B.V
Subjects
Applications of Mathematics
Burgers equation
Computational Mathematics and Numerical Analysis
Finite difference method
High resolution
Mathematical analysis
Mathematical Applications in Computer Science
Mathematical Applications in the Physical Sciences
Mathematics
Mathematics and Statistics
35F50
High resolution schemes
Compact finite difference schemes
65N35
Burgers equation
65M06
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Summary:In this article, non-standard compact finite difference schemes are constructed for the numerical approximation to first- and second-order derivatives. The proposed compact schemes have eighth order of accuracy and are tri-diagonal in nature, making use of a stencil smaller than those of conventional tri-diagonal compact finite difference schemes of the same order. They also possess high resolution properties and more resolving efficiency than conventional schemes. Some numerical experiments have been carried out, showing the good performance of the proposed schemes. Furthermore, the proposed schemes have been applied to solve with great efficiency the well-known Burgers equation.
ISSN:2238-3603
1807-0302
DOI:10.1007/s40314-024-02615-8