restart:

Eq1:=1/r*diff(r*diff(w(r),r),r)-(cos(z1))^2*(w(r)+1)-DP;

dsolve({Eq1});

bcs:=D(w)(0)=0,w(r2)=A1;

dsolve({Eq1,bcs},w(r)):

where z1, Dp, r2, A1 are constants.

how maple calculate exp(x) with e.g. 100000 decimal numbers

a divsion of the series x^k/k! with e.g. 1/25000!/25001 lasts longer than the exp(1.xx) calculation

is there a faster way to calculate exp(x) than with the x^k/k! series

thanks

(a) Design your own 3-stage explicit Runge-Kutta method with one-step error O(h4).

(b) Test your method by solving y′ = −y. Confirm that the global error in your numerical solution

is O(h3).

restart:

Eq1:=S*diff(f(x,t),x,t)+diff(f(x,t),x)^2-f(x,t)*diff(f(x,t),x$2)=diff(f(x,t),x$3);

BCs := {D[1](f)(0,t)=cos(t), f(0,t)=0,D[1](f)(L,t)=0};

ICs := {f(x,0)=0};

S:=10:L:=5:
smod3:= pdsolve(Eq1,ICs union BCs,numeric,range=0..L);

smod3:-plot(t=0,  color=red):

it seems to me that the problem is due to the mixed bcs. Any way around?

Cheers!

Good afternoon sir.

I am working on problems related to functions which require dynamic geometry program or

the Geometers sketch pad. I request to you to kindly suggest me with regard to the above cited query.

With thanks & Regards

M.Anand

Assistant Professor in Mathematics

SR International Institute of Technology,

Hyderabad, Andhra Pradesh, INDIA.

Dear Experts,

When I run this code in maple I am facing with "Error, (in dsolve/numeric/bvp) initial Newton iteration is not converging".

restart:
 
 unprotect('gamma');
 lambda:=5*10^5:
 mu:=0.003:
 beta:=4*10^(-10):
 delta:=0.2:
 alpha:=0.043:
 sigma:=alpha+delta:
 k:=6.24:
 gamma:=0.65:
 A[1]:=1:
 A[2]:=1:

ics := x[1](0)=1.7*10^8, x[2](0)=0,x[3](0)=400,psi[1](50)=0,psi[2](50)=0,psi[3](50)=0:

ode1:=diff(x[1](t), t)=lambda-mu*x[1](t)-(1-beta*x[1](t)*x[3](t)*(psi[1](t)-psi[2](t))/A[1])*beta*x[1](t)*x[3](t)+delta*x[2](t),
 diff(x[2](t), t) =(1-beta*x[1](t)*x[3](t)*(psi[1](t)-psi[2](t))/A[1])*beta*x[1](t)*x[3](t)-sigma*x[2](t),
 diff(x[3](t), t) =(1+psi[3](t)*k*x[2](t)/A[2])*k*x[2](t)-gamma*x[3](t),
 diff(psi[1](t), t) =-1+1/A[1]*beta^2*x[1](t)*x[3](t)^2*(psi[1](t)-psi[2](t))^2-psi[1](t)*(-mu+beta^2*x[3](t)^2*(psi[1](t)-psi[2](t))/A[1]*x[1](t)-(1-beta*x[1](t)*x[3](t)*(psi[1](t)-psi[2](t))/A[1])*beta*x[3](t))-psi[2](t)*(-beta^2*x[3](t)^2*(psi[1](t)-psi[2](t))/A[1]*x[1](t)+(1-beta*x[1](t)*x[3](t)*(psi[1](t)-psi[2](t))/A[1])*beta*x[3](t)),
> diff(psi[2](t), t) =1/A[2]*psi[3](t)^2*k^2*x[2](t)-psi[1](t)*delta+psi[2](t)*sigma-psi[3](t)*(psi[3](t)*k^2/A[2]*x[2](t)+(1+psi[3](t)*k*x[2](t)/A[2])*k),
> diff(psi[3](t), t) = 1/A[1]*beta^2*x[1](t)^2*x[3](t)*(psi[1](t)-psi[2](t))^2-psi[1](t)*(beta^2*x[1](t)^2*(psi[1](t)-psi[2](t))/A[1]*x[3](t)-(1-beta*x[1](t)*x[3](t)*(psi[1](t)-psi[2](t))/A[1])*beta*x[1](t))-psi[2](t)*(-beta^2*x[1](t)^2*(psi[1](t)-psi[2](t))/A[1]*x[3](t)+(1-beta*x[1](t)*x[3](t)*(psi[1](t)-psi[2](t))/A[1])*beta*x[1](t))+psi[3](t)*gamma;

sol:=dsolve([ode1,ics],numeric, method = bvp[midrich]);

Error, (in dsolve/numeric/bvp) initial Newton iteration is not converging

Please help me to solve this equation on Maple.

Hello,

I understand that the question is not really Maple related, but I still hope for some help.

See the worksheet below. I defined a pure sine wave and determined the complex Fourier coefficients for it which I used to plot the amplitude and power spectra. It is easy to see the relations in terms of amplitude and power between the time and frequency signal.

The Fourier Transform of the sine wave logically shows the Dirac distribution, but I can't see the relation in terms of amplitude and power to the original time signal. Taking the integral of the transformed signal (A) wil result in a step of Pi at w=-1 and again at w=1. What am I missing here?

Thanks

Download 20140127MaplePrime.mw

Hi everyone

I am currently trying to make my own simple package including a few procedures. So far I have been able to write some "code" that actually works when I open the document and hit "enter". I would, however, like to save the package so it can be accessed during any Maple session using the command "with". I have unsuccesfully tried to comprehend the Maple help pages regarding this question but I definitely don't want to mess things up.

This is what I have written:

mat := module ()
description "useful procedures for mathematics, physics and chemistry";
export AtomicWeight;
option package;

   AtomicWeight := proc (x) description "returns the average atomic mass of the naturally ocurring element";
   Units:-AddSystem(NewSystem, Units:-GetSystem(SI), u);
   return evalf(ScientificConstants:-Element(x, atomicweight, system = NewSystem, units))
   end proc

end module;

What should I do to save it correctly?

Thank in advance,
Mads

I received an unexpected error message when trying to minimize a function: evaluating

returns the error message

Error, (in @) too many levels of recursion

Why am I getting this message?  It's hard for me to see how minimizing a function involves recursion, unless Maple is trying to iteratively approximate a solution.

Mapleprimes_Integral.mw

I have a question regarding following problem:

Download Mapleprimes_Integral.mw

Hi MaplePrimers!

I have a simulation in MapleSIM, exported as a compiled procedure in maple using -LinkModel(), and -GetCompiledProc.

I'm trying to do parameter estimation on my MapleSIM model.  Within a optimization scheme, I call the MapleSIM model, and it will output a curve.  Using a least squares method, I compare this measurements to synthetic experimental data (I know the actual values), and generate an objective function.  The optimization algorithm will try different parameter values, and try to minimze the objective function.  When the curves are exactly the same, the objective function will be zero.

The problem I am having is certain parameter sets will cause the model to require very small steps.  I wish to put a timeout on these experiments, because speed is important.  However, I would also like to see the results up to the point of requiring very small steps.  For timeout, I was using code along the lines of:

out:= timelimit(30,cProc(params = PData)); #simulate with 30s limit

where PData are the parameter guessses, and cProc is the compiled MapleSim model.

I would like 'out' to be assigned whatever the results were after 30 seconds, even if the model had not finished integrating.

Thanks in advance for any help!

hi,

     there is a common  differential equation in my maple note,the solution of the eq. can be expressed by

associated Legendre function(s),but i get a result by hypergeometric representation.how i can translate the later into a  single Legendre fun？

 Thank you in advance  

Download question_12.19.mw

I have an ipad air 16G running ios 7.0.4 and downloaded the MaplePlayer APP.  t seems to crash on several of the routines for example, "Approximaing Sphere" and "Linear System Tutor". The app was last updated in 2011.  Do you have plans to any upgrades plan in the near future?

Hi MaplePrimers,

I'm trying to solve a system of algebraic equations using 'solve' [float].  I'd prefer to use 'solve' over 'fsolve', as 'solve' solves my system in about 0.05s, whereas fsolve takes about 5 seconds.  I need to solve the system repeatedly at a different points, so time is important.  I don't know why there is such a large difference in time ... 

I have a few piecewise functions of order 3 to 5.  It solves fine with the other (piecewise) equations, but adding one piecewise function which gives me an error while trying to solve:

Error, (in RootOf) _Z occurs but is not the dependent variable.

I think this is due to solve finding multiple solutions.  Is there a way to limit solve to only real solutions?

Thanks in advance!