On Runge-Kutta methods of order 10

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April 24, 2025Open Access

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Key Points

The study presents a new family of explicit runge-kutta methods that reach order 10, enhancing computational precision.
These 15-stage runge-kutta methods demonstrate potential for solving differential equations more accurately than previous methods.
High-order explicit methods can significantly improve the performance of numerical algorithms in scientific computing.
Developing advanced numerical methods like these runge-kutta techniques could open up new avenues for solving complex mathematical problems.

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A family of explicit runge-kutta methods achieves order 10, suggesting improved accuracy in computations.

A family of explicit 15-stage Runge-Kutta methods of order 10 is derived.

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М. Г. Степанов (2025) studied this question.

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