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This research focuses on enhancing numerical methods for solving fourth-order initial value problems with derivative dependence.

March 3, 2026Open Access

Explicit Runge–Kutta–Nyström-Type Schemes for Fourth-Order Systems y(4)=f (x, y, y′)

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This work demonstrates improved numerical solutions for fourth-order systems, highlighting computational efficiency in vibroacoustic dynamics.

This research focuses on enhancing numerical methods for solving fourth-order initial value problems with derivative dependence.
Developed an explicit s-stage method incorporating first derivatives into internal stage approximations.
Derived algebraic order conditions up to the seventh order for the new methods.
Constructed a particular pair of orders 6(4) with reduced stage cost compared to conventional methods.
The new schemes achieved higher accuracy with fewer function evaluations.
Demonstrated superior performance over existing Runge-Kutta pairs in structural and vibroacoustic dynamics.
Showed effectiveness in models with velocity-dependent damping and coupled interactions.

Alqahtani et al. (2026) studied this question.

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This work demonstrates improved numerical solutions for fourth-order systems, highlighting computational efficiency in vibroacoustic dynamics.