Solver

Non-linear Routing Solver Using RK Methods

Overview

This solver addresses non-linear routing equations by integrating user-specified ordinary differential equations (ODEs). It leverages adaptive and fixed-step Runge-Kutta methods to balance accuracy and computational efficiency.

Integration Methods

• RK45 (Dormand-Prince): The default solver is an adaptive Runge-Kutta-Fehlberg 4(5) method (RK45), which dynamically adjusts step sizes to meet user-defined error tolerances. This ensures accurate solutions for stiff or highly non-linear routing problems.
• RK4 Fixed Step: For performance optimization, users can select predefined levels where a classical Runge-Kutta 4th-order (RK4) fixed-step method is applied. This provides faster computation when strict adaptive control is not critical.

User Configuration

• Tolerances: Users can specify absolute and relative error tolerances, which guide the adaptive RK45 solver.
• Performance Levels: Users may select levels to allow RK4 fixed-step integration in less sensitive portions of the solution, trading some precision for speed.

Library Used

The solver is implemented using Boost.Numeric.ODEInt, a C++ library providing flexible and efficient ODE integration with support for both adaptive and fixed-step Runge-Kutta methods.

Applications

• Network routing simulations
• Non-linear system analysis
• Performance-sensitive ODE modeling

References

• Boost.Numeric.ODEInt Documentation: https://www.boost.org/doc/libs/1_55_0/libs/numeric/odeint/doc/html/index.html