How can I overcome errors in RK4 due to linearly interpolated data?

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SUMMARY

The discussion centers on overcoming errors in the Runge-Kutta 4th order (RK4) method caused by linearly interpolated data in ordinary differential equation (ODE) simulations. Users reported significant accumulating errors when using linear interpolation between sampled data points. Alternatives such as Euler integration were considered, but participants emphasized the desire to maintain higher-order accuracy in their simulations. The sensitivity of the RK4 method to step length was highlighted as a critical factor in achieving accurate results.

PREREQUISITES
  • Understanding of ordinary differential equations (ODEs)
  • Familiarity with Runge-Kutta methods, specifically RK4
  • Knowledge of numerical integration techniques
  • Experience with data interpolation methods
NEXT STEPS
  • Investigate advanced interpolation techniques, such as spline interpolation
  • Explore adaptive step size methods for RK4 integration
  • Learn about error analysis in numerical methods for ODEs
  • Research alternative higher-order integration methods, such as Runge-Kutta-Fehlberg
USEFUL FOR

Mathematicians, physicists, and engineers involved in numerical simulations of ordinary differential equations, particularly those seeking to improve the accuracy of RK4 methods in the presence of sampled data.

Liferider
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I am simulating an ODE where the differential function is a function of sampled data points and are having trouble obtaining data in between sampled points (for the step computations of RK4). The first thing that I tried was to linearly interpolate the data, but that introduced large accumulating errors in the simulation. Is there a way to circumvent this?

One possibility of course, is to use Euler integration with the appropriate step length, but it would be nice to use a higher order scheme if possible.
 
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Don't bother, just very sensitive regarding step length.
 

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