How can I overcome errors in RK4 due to linearly interpolated 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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