## 5408 Reputation

17 years, 226 days
Munich, Germany

## Examples from DirectSearch...

@mmcdara

Find some examples from the package (which is free) in the attached pdf. Certainly it solves the example in the paper (at the end).

Examples_from_DirectSearch.pdf

## unfortunately...

@J F Ogilvie unfortunately not, I was trying to understand the task

## DirectSearch...

Probably the best would be to use https://www.maplesoft.com/applications/view.aspx?SID=101333, stable and validated, instead of trying to translate a 40 year old code

## arc length?...

Or more simple: you ask for the length of the graph of an oscillating (damped) function cos(x)*exp(r*x+s), yes?

## yes...

@mmcdara yes, I meant something like that - and it may be quickly more complicated to write it down in Maple than writing down the Math (as far I understand you here: do a linear change of variables and re-arrange terms)

## that...

Essentially you have to write down the formal steps of the proof you know from lectures, now using Maple's notations

## please post code, not images...

please post code (as text or uploading a Maple sheet), not images

and your assumptions on t should be stated

## even for a simple case ......

Even for a simple case you will get no answer, say Int(sqrt(1/(2*ln(t)+t)), t = 1 .. 2)

## 2020...

I have installed 2020.0, which I do not want to change it for that test, so can not show it

## "save as"...

@Carl Love I suppose that on Windows the filename can be catched from system libraries, since the dialog "save as" automatically provides the name

## Maple 2020...

@tomleslie he is using Maple 2019, and in Maple 2020 I get your result without the Physics extension

u(x) = 1/10*piecewise(x < 0,(-1+I+(1+I)*3^(1/2))*5^(1/2)*(22*I*x+(16*x^2+44*x-1
)^(1/2)-I)^(1/6)*2^(1/3)/x^(1/3),x = 0,20,0 < x,2*(-1)^(1/12)*5^(1/2)*2^(5/6)/x
^(1/3)*(22*I*x+(16*x^2+44*x-1)^(1/2)-I)^(1/6))

## neat!...

@vv a neat elaboration!

## some remarks...

There may be many reasons for "errors".

For example you provide only a small number of decimals for your constants (4 - 5) while sometimes you provide 16 decimals. It might be better to provide at least 16 for all (and more if it turms out that higher precision is used) to reduce rounding errors

This is a bit related to a mathematical fact: generically you can expect discrete solutions if using n=13 equations and n variables (discrete = isolated n-tuples in n-space each giving a solution). But even if there would be only discrete solutions there might be none, especially over the Reals (think pf a parabola).

And if feeding the solutions there will be a (numerical) error. One has to judge whether it can be accepted or not - for example a very steep function with a zero z0 may have a large absoluet error in that while it can be accepted because it is small in a relative sense (and the "best" approximation).

From you last eq13 and your remark "must be positive" it follows that u_C1 is between ionic=0 and ionic=infinity, i.e. roughly between 0.58 and 0.97

## exp = parabola ?...

As far as I can see you want to solve something like exp(r*x)= a*x^2 + b*x + c. You can not expect a "closed" form (but you can do it using fsolve after feeding numerical values for you parameters)

## hm...

Do not use data frames.

I converted your CSV to xlsx (and corrected the field name)

For your large file I get the error "Error, (in ExcelTools:-Import) out of memory error while processing result" in Maple 2017, for 2020 it results in some non-processing without error message or warning, for your smaller file it works, in both cases I used the standard interface (*.mw)

So - as you guessed - the file may be too large (at least for my machine)

Your link does not work for me, may be it uses services which have blocked for my machine or through my firewall

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