@acer I have now achieved what I wanted with my model. I have been frustrated by this for a while, so your help has been a major relief. Thank you very much.

@acer I have now achieved what I wanted with my model. I have been frustrated by this for a while, so your help has been a major relief. Thank you very much.

@acer 

I have tried the numapprox with very nice results. The match between the red and green curve is perfect for my need. However, I am a bit confused with the output of my integrations. What does 0.I mean? Something to do with higher order terms? Can I have Maple remove these automatically?

@acer 

I have tried the numapprox with very nice results. The match between the red and green curve is perfect for my need. However, I am a bit confused with the output of my integrations. What does 0.I mean? Something to do with higher order terms? Can I have Maple remove these automatically?

I have attached my example. I found that polynomial approximation works reasonably well if it is done separatly (?) in the two regions -1>r>0 and 0>r>1.

ExampleMaplePrime.mw

I have attached my example. I found that polynomial approximation works reasonably well if it is done separatly (?) in the two regions -1>r>0 and 0>r>1.

ExampleMaplePrime.mw

If I perform numeric approximation, will I still end up with a function? I need a function for further analysis, such as integration. An error of 1e-3 would suffice for my work. 

I have shown an example of a function in the below image. It contains only one variable (r) but many trigonometric functions. It should be possible to find a simpler function with the same "path" from r=-1 to r=1.

I perform an 8th order polynomial approximation and get this:

If I perform numeric approximation, will I still end up with a function? I need a function for further analysis, such as integration. An error of 1e-3 would suffice for my work. 

I have shown an example of a function in the below image. It contains only one variable (r) but many trigonometric functions. It should be possible to find a simpler function with the same "path" from r=-1 to r=1.

I perform an 8th order polynomial approximation and get this:

Even better. Thank you.

Even better. Thank you.