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

Allaberen Ashyralyev, Ibrahim Mohammed Ibrahım

BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS, 2024

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DOI 10.31489/2024m4/18-30

Data confidence 70 medium

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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.