An Efficient Non-Standard Numerical Scheme Coupled with a Compact Finite Difference Method to Solve the One-Dimensional Burgers’ Equation
This article proposes a family of non-standard methods coupled with compact finite differences to numerically integrate the non-linear Burgers’ equation. Firstly, a family of non-standard methods is derived to deal with a system of ordinary differential equations (ODEs) arising from the semi-discret...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-06-01
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| Series: | Axioms |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2075-1680/12/6/593 |
| Summary: | This article proposes a family of non-standard methods coupled with compact finite differences to numerically integrate the non-linear Burgers’ equation. Firstly, a family of non-standard methods is derived to deal with a system of ordinary differential equations (ODEs) arising from the semi-discretization of initial-boundary value partial differential equations (PDEs). Further, a method of this family is considered as a special case and coupled with a fourth-order compact finite difference resulting in a combined numerical scheme to solve initial-boundary value PDEs. The combined scheme has first-order accuracy in time and fourth-order accuracy in space. Some basic characteristics of the scheme are analysed and a section concerning the numerical experiments is presented demonstrating the good performance of the combined numerical scheme. |
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| ISSN: | 2075-1680 |