The compact eighth-order of approximation difference schemes for fourth-order differential equation

Authors

DOI:

https://doi.org/10.31489/2024m4/18-30

Keywords:

Taylor’s decomposition on five points (TDFP), LNBVPs, DSs, approximation, numerical experiment

Abstract

Local and nonlocal boundary value problems (LNBVPs) related to fourth-order differential equations (FODEs) were explored. To tackle these problems numerically, we introduce novel compact four-step difference schemes (DSs) that achieve eighth-order of approximation. These DSs are derived from a novel Taylor series expansion involving five points. The theoretical foundations of these DSs are validated through extensive numerical experiments, demonstrating their effectiveness and precision.

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Published

2024-12-30

How to Cite

Ashyralyev, A., & Ibrahim, I. (2024). The compact eighth-order of approximation difference schemes for fourth-order differential equation. Bulletin of the Karaganda University. Mathematics Series, 116(4), 18–30. https://doi.org/10.31489/2024m4/18-30

Issue

2024 (116) 4

Section

MATHEMATICS