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March 25, 2026SymmetryOpen Access

Runge–Kutta Schemes for Addressing Left-Endpoint Singularities

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Authors

NANadiyah Hussain AlharthiImam Mohammad ibn Saud Islamic UniversityRARubayyi T. AlqahtaniImam Mohammad ibn Saud Islamic UniversityTSTheodore E. SimosDemocritus University of Thrace

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Implication

This approach addresses singularities in initial value problems, improving numerical method efficiency.

Key Points

  • The aim is to enhance the efficiency of Runge-Kutta methods when dealing with singularities at the initial point.
  • Propose an alternative Runge-Kutta approach to shift the first evaluation away from singularities
  • Establish order conditions for algebraic order six
  • Construct an eight-stage Runge-Kutta scheme
  • Compare performance against classical Runge-Kutta pairs of orders 6(5) and 8(7)
  • The new method significantly improves efficiency compared to classical approaches in singularity scenarios
  • Outperforms existing Runge-Kutta methods in practical applications involving initial-point singularities

Cite This Study

Alharthi et al. (2026) studied this question.

synapsesocial.com/papers/69c37b33b34aaaeb1a67d68ehttps://doi.org/10.3390/sym18030539
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