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tsunamiBTP

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16 years, 302 days
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Trouble solving a transcendental equatio...

tsunamiBTP 292 Maple 12
solve
December 24 2017
1 2

I am still working on the worksheet linked below.  But I have run into trouble solving the equation symbolicly within for the variable t.  I think this is due to the fact there are multiple solutions and the commands I employed through the GUI interface is not capable of handling this issue?  For example, the solutions for sin(pi*t/T) would be N*T.  MAPLE is simply stating t=0.  So I think this is why my solutions are failing to produce results.

What other commands should I be employing?

solving_transcendental.mw

fsolve versus RootFinding...

tsunamiBTP 292 Maple 12
rootfinding fsolve
December 15 2017
1 3

I executed finding the roots of the derivative of a series expansion containing 500 terms.  I did it 2 ways.  The 1st using fsolve & the 2nd using RootFinding.  The fsolve took over 20 minutes to find a single root within a specified range while the RootFinding took less than 60 seconds to find all roots within a larger range.  I do not know of the inner mechanisms of either command, but why is this the case?  Why would the algorithms differ?  My results are in the link below.

fsolve_vs_RootFinding.mw

simplify command expresses results by un...

tsunamiBTP 292 Maple 12
sum simplify special-function
December 12 2017
0 0

Below is MAPLE code to simplify a series.  MAPLE expresses the result in terms of functions which many people are not familiar with.  Is there a way to express the answer in terms of more conventional functions expecially if N is a positive integer?


 

Cn := ((-I)*(1/2))*(2*(I*Pi*n*tau-(2*I)*Pi*n)*cos(Pi*n*tau/T)-T*(2*I)*sin(Pi*n*tau/T)+(4*I)*Pi*n)/(Pi^2*n^2); S4 := a[0]+sum(Cn*sin(2*Pi*n*x/T), n = 1 .. k); a[0] := 0; T := 4; tau := 2; Cn; S5 := unapply(S4, k, x); T := simplify(S5(N, x))

convert(T, StandardFunctions);

(-polylog(2, exp(-((1/2)*I)*Pi*(x-1)))*N^2-exp(-((1/2)*I)*Pi*N*(x+1))*LerchPhi(exp(-((1/2)*I)*(x+1)*Pi), 2, N)*N^2+polylog(2, exp(((1/2)*I)*(x+1)*Pi))*N^2+exp(-((1/2)*I)*Pi*N*(x-1))*LerchPhi(exp(-((1/2)*I)*Pi*(x-1)), 2, N)*N^2+polylog(2, exp(-((1/2)*I)*(x+1)*Pi))*N^2-exp(((1/2)*I)*Pi*N*(x+1))*LerchPhi(exp(((1/2)*I)*(x+1)*Pi), 2, N)*N^2-polylog(2, exp(((1/2)*I)*Pi*(x-1)))*N^2+exp(((1/2)*I)*Pi*N*(x-1))*LerchPhi(exp(((1/2)*I)*Pi*(x-1)), 2, N)*N^2+exp(((1/2)*I)*Pi*N*(x+1))-exp(((1/2)*I)*Pi*N*(x-1))+exp(-((1/2)*I)*Pi*N*(x+1))-exp(-((1/2)*I)*Pi*N*(x-1))-I*exp(-((1/2)*I)*x*Pi*N)*LerchPhi(exp(-((1/2)*I)*x*Pi), 1, N)*N^2*Pi-I*ln(1-exp(-((1/2)*I)*x*Pi))*N^2*Pi+I*exp(((1/2)*I)*x*Pi*N)*LerchPhi(exp(((1/2)*I)*x*Pi), 1, N)*N^2*Pi+I*ln(1-exp(((1/2)*I)*x*Pi))*N^2*Pi-I*exp(((1/2)*I)*x*Pi*N)*N*Pi+I*exp(-((1/2)*I)*x*Pi*N)*N*Pi)/(N^2*Pi^2)

 (1)

``


 

Download simplify.mw

fsolve interval resolution...

tsunamiBTP 292 Maple 12
December 12 2017
2 11

When attempting to numerically solve for a function using fsolv it is possible that the function has multiple roots.  So to focus on a particular region you specify a range such as:

xmax := fsolve(S, x = 0 .. 1/2)

Is it possible fsolve may not resolve the solution due to the fact that delta x is not small enough or does fsolve autonomously adjust delta x in order to find the solution?  If not, how do you manually dictate the delta x for the interval specified?

value & evalf syntax issues?...

tsunamiBTP 292 Maple 12
syntax value evalf
December 10 2017
1 0

Below is a link to my worksheet.  I am attempting to evaluate a Fourier series for a particular number of terms & at a specific location xmax.  As far as I can tell xmax is assessed correctly.  Howver, when I go to evaluate the Fourier series for x = xmax using either the 'value' or 'evalf' command they do on seem to recognize that x = xmax.

So I am guessing I must have some syntax problem.  Can anyone show me what I have wrong?

command_syntax.mw

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