Exponentially fitted open Newton-Cotes differential methods as multilayer symplectic integrators

Area of Science:

• Numerical analysis
• Computational physics
• Differential equations

Background:

• Classical Newton-Cotes methods are known for their multilayer symplectic structures.
• Previous work established these structures for open and closed methods.
• Hamiltonian systems require volume-preserving integrators for accurate long-term simulations.

Purpose of the Study:

• To investigate exponentially fitted open Newton-Cotes differential methods of orders two, four, and six.
• To demonstrate that these new integrators preserve phase space volume.
• To show their compatibility with multilayer symplectic structures.

Main Methods:

• Construction of exponentially fitted open Newton-Cotes differential methods.
• Theoretical analysis to prove volume preservation properties.
• Conversion of integrators into multilayer symplectic structures.
• Application to a numerical example of a Hamiltonian system.

Main Results:

• The developed exponentially fitted open Newton-Cotes methods preserve volume in the phase space.
• These integrators can be successfully converted into multilayer symplectic structures.
• The numerical example confirmed the effectiveness of the proposed differential method.

Conclusions:

• Exponentially fitted open Newton-Cotes methods are effective volume-preserving integrators for Hamiltonian systems.
• These methods extend the applicability of classical symplectic integrators.
• The study validates the theoretical findings with a practical numerical demonstration.