Nick_99

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These are questions asked by Nick_99

I have the following function:

f:=t->862.979774+1825.011621/([1+1.54943476*e^(-677.0138344*t)]^(131537/203808))

Is there any way Maple can calculate the indefinite integral of f(t)? I have tried integrating f(t) in a range t=tmin..tmax numerically using dsolve/numeric and plotting the numeric integral and I am satisfied with the result, but I would much prefer an analytic integration so that I obtain some function y(t) that I can later use which will be the indefinite integral of f(t).

So far, I have tried unsuccessfully to obtain an indefinite integral of f(t) using int and dsolve. Thanks in advance.

I have the following piece of code:

beta := 16250.25391;

tlow := 11.92817468;

y0 := t -> 1/4*4^(7/8)/(beta*(tlow - t))^(1/8);

r0 := 1;

r2 := 1.194444444;

r3 := -2.071877530;

dyr := t -> M*(-2*r0*diff(y0(t), t)/y0(t)^3 + 2*r2*y0(t)*diff(y0(t), t) + 4*r3*y0(t)^3*diff(y0(t), t));

plot(dyr(t))

Everything seems to work out fine until this point and I obtain a good plot. The problem occurs when I try calling the value of dyr at a specific point t. Here is an example:

dyr(5)
Error, (in dyr) invalid input: diff received 5, which is not valid for its 2nd argument

I understand there is something wrong with the diff part. I tried writing the following simple code and I have the same problem.

y := t -> t^2

z := t -> diff(y(t), t)

z(1);
Error, (in z) invalid input: diff received 1, which is not valid for its 2nd argument

I start with a function that has only one argument and it seems like introducing the diff requires that I use two arguments. y0 is a function of t solely and I would like dyr to have the same argument, so that I can call dyr(t) at any point t I want. Please take a look at this. Thanks in advance.

I have the following link with data that I want to import to Maple and plot... any ideas how I can do that? Thanks.

https://www.gw-openscience.org/GW150914data/P150914/fig1-observed-H.txt

I have a piece of code that solves a differential equation numerically and plots the solution, but I also want to store my values for the solution so that I can later call them easily. I want to be able to save my values for xphi for all t from 0 to 11 - not necessarily with the same variable name, it could be some k(t) - so that later when I type eg k(10) Maple gives me the value of xphi at t=10. I assume the code only requires a slight modification, but still I haven't been able to find a way to do this. Here is the corresponding piece of code. Thank you in advance.

xodephi := {diff(x(t), t) = 16250.25391*(1 - (487*x(t))/168 + 4*Pi*x(t)^(3/2) + (274229*x(t)^2)/72576 - (254*Pi*x(t)^(5/2))/21 + (119.6109573 - (856*ln(16*x(t)))/105)*x(t)^3 + (30295*Pi*x(t)^(7/2))/1728 + (7.617741607 - 23.53000000*ln(x(t)))*x(t)^4 + (535.2001594 - 102.446*ln(x(t)))*x(t)^(9/2) + (413.8828821 + 323.5521650*ln(x(t)))*x(t)^5 + (1533.899179 - 390.2690000*ln(x(t)))*x(t)^(11/2) + (2082.250556 + 423.6762500*ln(x(t)) + 33.2307*ln(x(t)^2))*x(t)^6)*x(t)^5, diff(xphi(t), t) = 5078.204347*x(t)^(3/2), x(0) = 0.03369973351, xphi(0) = a}:  #xphi(10.92469316) = 0}:

sol := dsolve(xodephi, parameters=[a], numeric):

ff:=proc(A)
  sol(parameters=[A]);
  eval(xphi(t), sol(10.92469316))
end:

A:=fsolve(ff);
sol(parameters=[A]);
sol(10.92469316);

-467.1843838

 

[a = -467.1843838]

 

[t = 10.92469316, x(t) = HFloat(0.061040830524973895), xphi(t) = HFloat(1.6909911249030074e-9)]

(1)

plots:-odeplot(sol, [t,xphi(t)], t=0..11);

 

plots:-odeplot(sol, [t,x(t)], t=0..11);

 

 

 

I want to solve the following system of differential equations to find xphi, but I seem to be doing something wrong because I get an error message.

 

xodephi := {diff(x(t), t) = 16250.25391*(1 - (487*x(t))/168 + 4*Pi*x(t)^(3/2) + (274229*x(t)^2)/72576 - (254*Pi*x(t)^(5/2))/21 + (119.6109573 - (856*ln(16*x(t)))/105)*x(t)^3 + (30295*Pi*x(t)^(7/2))/1728 + (7.617741607 - 23.53000000*ln(x(t)))*x(t)^4 + (535.2001594 - 102.446*ln(x(t)))*x(t)^(9/2) + (413.8828821 + 323.5521650*ln(x(t)))*x(t)^5 + (1533.899179 - 390.2690000*ln(x(t)))*x(t)^(11/2) + (2082.250556 + 423.6762500*ln(x(t)) + 33.2307*ln(x(t)^2))*x(t)^6)*x(t)^5, diff(xphi(t), t) = 5078.204347*x(t)^(3/2), x(0) = 0.03369973351, xphi(10.92469316) = 0}

xsolphi := dsolve(xodephi, numeric)

Error, (in dsolve/numeric/bvp) precision is insufficient for required absolute error, suggest increasing Digits to approximately 25 for this problem

 

Later, I am interested in plotting xphi for t ranging from (11.92469316 - 1) to 11.92469316, but first I need to obtain a numerical solution for xphi in this region. Any advice?

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