How can the accuracy in the computed solution in the ApproxFun Tutorials be adapted/changed? Is there a way top set the number of basis functions being used for e.g. a coarse, intermediate and fine scale approximation? How would one perform a test of the reduction of discretization error as the number of basis functions is increased?

Why does backslach require a tolerance setting for linear problems? What is this tolerence used?

Thereâ€™s just a tolerance flag that measures the error in residual

For spectral methods itâ€™s not that important as the DOF donâ€™t increase that much if you lower the tolerance. Your â€ścourseâ€ť â€śintermediateâ€ť â€śfineâ€ť language is more relevant for h-refinement not p-refinement

Clear, thanks, understood.

Still, being naughty and stubborn, is there a way to override the default way of working with ApproxFun? I would like to set (predetermine, fix) the number of expansion terms prior to the linear solve. My interest here is two-fold. First, performing a study of discretization error. Second, seek ways to use ApproxFun to implement a harmonic balance method. In this method, one typically predetermines the number of harmonics.

I am not sure whether using

```
x = points(S, n)
```

as done in this Example

goes in the direction I am interested in.

Additional input is very much appreciated.

ClassicalOrthogonalPolynomials.jl might be better suited for your needs

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Many thanks. I will give it a look.