Derivation of Embedded Diagonally Implicit Methods for Directly Solving Fourth-order ODEs

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Omar Mohammed Saleh
Firas Adel Fawzi
Kasim Abas Hussain
Nizam G. Ghawadri

Abstract

EDIRKTO, an Implicit Type Runge-Kutta  Method of Diagonally Embedded pairs, is a novel approach presented in the paper that may be used to solve 4th-order ordinary differential equations of the form . There are two pairs of EDIRKTO, with three stages each: EDIRKTO4(3) and EDIRKTO5(4). The derivation techniques of the method indicate that the higher-order pair is more accurate, while the lower-order pair provides superior error estimates. Next, using these pairs as a basis, we developed variable step codes and applied them to a series of -order ODE problems. The numerical outcomes demonstrated how much more effective their approach is in reducing the quantity of function evaluations needed to resolve fourth-order ODE issues.

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How to Cite
[1]
Saleh, O.M. et al. 2024. Derivation of Embedded Diagonally Implicit Methods for Directly Solving Fourth-order ODEs. Ibn AL-Haitham Journal For Pure and Applied Sciences. 37, 1 (Jan. 2024), 375–385. DOI:https://doi.org/10.30526/37.1.3288.
Section
Mathematics

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