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September 10, 2025Ibn AL- Haitham Journal For Pure and Applied ScienceOpen Access

Efficient Embedded Diagonal Implicit Runge-Kutta Method for Directly Solving Third Order ODEs

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Authors

FFFiras A. FawziHGHadeer M. GlobeNGNizam G. Ghawadri

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Overview

This study reveals new implicit runge-kutta processes for third order odes, suggesting enhanced accuracy through a novel embedded method.

Key Points

  • The proposed ERKTDIO method outperforms traditional methods in solving third order odes with improved accuracy and efficiency.
  • A fifth-order method with three stages and a sixth-order method with four stages are derived, showcasing superior performance.
  • Utilizing variable step-size codes, the study demonstrates the effectiveness of the new methods compared to existing solutions.
  • Higher-order methods achieved high accuracy while lower-order methods provided optimal error estimates, validating their practical applications.

Cite This Study

Fawzi et al. (2024) studied this question.

synapsesocial.com/papers/68c1e07554b1d3bfb60fcddehttps://doi.org/10.30526/37.2.3409
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