The lspline will support >...extrapolated beyond the ends of your data range < like the calculated vector of the Odesolve... even so, the red message "Solution outiside the argument". For surface plots, smoothing is generally desired if the data don't come out of functions.
1. Fourier mask smoothing
2. Fourier circular convolution
3. smoothing loess
4. smoothing ksmooth
5. polyline smoothing
are some suggestions as demonstrated in the attached, applied on the Z matrix level. In the case(s) the X, Y planes are not grids, smoothing might apply on those planes as well. What I'm saying by reverse conclusion is that the data should be first smoothed if necessary, then splined afterward, whereas cubic splines interpolate cubic between the points.
If your 3 spline project does not concern surface, please discard.
jmG