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October 20, 2025Open Access

Multi-order Runge-Kutta methods or how to numerically solve initial value problems of any order

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Authors

PLPetronijevic Loris

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Overview

This paper introduces multi-order Runge-Kutta methods, improving accuracy for initial value problems while highlighting convergence and stability.

Key Points

  • Multi-order Runge-Kutta methods improve accuracy in solving initial value problems without rewriting them.
  • The new methods establish convergence and order of consistency, enhancing existing numerical techniques.
  • Properties of linear stability are explored to better define explicit and implicit Runge-Kutta methods.
  • This approach allows for a deeper understanding of higher-order problems in numerical analysis.

Cite This Study

Petronijevic Loris (2025) studied this question.

synapsesocial.com/papers/68f6379bb481a140a36cf454https://doi.org/10.48550/arxiv.2509.23513
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