Hello,

I have a problem using the NonlinearFit function from the Statistics package in Maple 2018.

I want to fit an exponential function which is non-linear in the parameters. The function in itself is working fine but i want to implement an extra condition on the parameters that are fitted. I already implemented the range of each parameter which is from 0 to 1, but I also want to implement the following condition:

a + b + c = 1.0
 

This is the code that i am using:

with(Statistics);
X := Vector([0, 100, 200, 300, 400, 500], datatype = float);
Y := Vector([0.2e-2, 0.5e-2, 0.7e-2, 0.75e-2, 0.77e-2, 0.8e-2], datatype = float);
nlfit := NonlinearFit(epsfunc, X, Y, t, parameterranges = [a = 0 .. 1, b = 0 .. 1, c = 0 .. 1], initialvalues = [a = .2, b = .2, c = .2], output = [parametervalues, leastsquaresfunction]);

It there a way to implement the additional condition that a+b+c=1.0?

Thanks!

Joa

Edit:

Epsfunc is the result of solving an ODE using dsolve:

the following code is used:

restart;

eq1 := x(t)+(t1+t2)*(diff(x(t), t))+t1*t2*(diff(x(t), t, t)) = (n1+n2)*(diff(eps(t), t))+(n1*t2+n2*t1)*(diff(eps(t), t, t));
tr := n1*n2*(E1+E2)/((n1+n2)*E1*E2);
x := proc (t) options operator, arrow, function_assign; x0 end proc;
solution := dsolve({eq1, eps(0) = x0/(E1+E2), (D(eps))(0) = x0*((n1/E1+n2/E2)/(n1+n2)-1/(E1+E2))/tr}, eps(t)); assign(solution);

E := 500;
E1 := a*E; E2 := b*E; t1 := 100; t2 := c*t1; n1 := E1*t1; n2 := E2*t2; x0 := 2;
epsfunc := eval(eps(t));
 

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D^m u(x,t)=u''(x,t)-u^2 (x,t), where n-1< m < n 

IC: u(x,0)=1+sin(x), and u'(x,0)=0

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Solve: by variation of parameters.

x³y’’’ – x²y’’ − 2xy’ + 6y = x²

Use any software, e.g. Maple, as an aid in computing roots of the auxiliary equation and the Wronskian-based determinants W, W1, W2, W3

I was able to hand calculate the roots as [m₁ = 3, m₂ = 2, m₃ = -1]
 

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Lets say I have a circle with the eqn 

x^2 + y^2 - 10*x - 75 = 0

Is there a command which would allow me to convert the above to (x-5)^2+y^2=100 ? 

I have tried to both collect, factor but neither of these work for obvious reason. 

So any idea/surgestion on which command one could use? 

Many thanks in advance.  

i have try to solve these eq by maple 

and i got these errors 

new2fornet.maple

simplify(series(sin(g(x)),x=0,4));

sin(g(0)) + cos(g(0))*D(g)(0)*x + (-1/2*sin(g(0))*D(g)(0)^2 + 1/2*cos(g(0))*(D@@2)(g)(0))*x^2 + (1/6*(-D(g)(0)^3 + (D@@3)(g)(0))*cos(g(0)) - 1/2*sin(g(0))*(D@@2)(g)(0)*D(g)(0))*x^3 + :-O(1)*x^4

and I'd like to give the various values for g to evaluate the series. That is, I know g and it's derivatives at 0.

Maple 2019.2.

These two expressions are mathematically equivalent:

But simplify(expr1-expr2) does not give zero where simplify(convert(expr1,trig)-expr2) does.

Is this normal behavior or can be expected sometimes? As a user I would have expected Maple internally to figure all of this itself. Compare to Mathematica:

Is there a different command in Maple that will show mathematical equivalence of two expressions to try other than simplify?

Thanks
 

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Solving_ODE.mw

Here is an example.  How would I solve this non-homogeneous system of ODEs

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Source of interest in this topic.  There is a problem with drawing a cylinder. I draw a cylinder using the arrow function as follows:

cylinder := seq(arrow(`<,>`((L[1][i]+L[4][i])*(1/2), (L[2][i]+L[5][i])*(1/2), (L[3][i]+L[6][i])*(1/2)), `<,>`(-(L[1][i]+L[4][i])*(1/2)+(L[7][i]+L[10][i])*(1/2), -(L[2][i]+L[5][i])*(1/2)+(L[8][i]+L[11][i])*(1/2), -(L[3][i]+L[6][i])*(1/2)+(L[9][i]+L[12][i])*(1/2)), width = 1, color = green, head_length = 0, head_width = 0, length = VectorNorm(`<,>`((L[1][i]+L[4][i])*(1/2)-(L[7][i]+L[10][i])*(1/2), (L[2][i]+L[5][i])*(1/2)-(L[8][i]+L[11][i])*(1/2), (L[3][i]+L[6][i])*(1/2)-(L[9][i]+L[12][i])*(1/2)), 2), transparency = 0.), i = 1 .. N+1):

(L [j], j = 1..12 - the coordinates of the red points on the cylinder).


But, as you can see, because of the faces, everything does not turn out very smoothly. Is there a way to display the cylinder smoothly, but so that without too much computing resources, ie no more resource than a "arrow"?

Hai

Help required to plot the graphs for system  difference schemes .

 I am attaching the codes and sample graphs and  maple query but still getting  error.

here is the codes 

restart;
restart; Digits := 1;
Pr:=0.01:E:=1:a:=0:N:=10:

`&Delta;t`:=0.01:`&Delta;y`:=0.01:

#Discritization scheme

for i from 1 by 1 while i<=N do;  
end:
for j from 0 by 1 while j<=N do;
end:

eq1[i, j] := (U[i, j+1]-U[i, j])/`&Delta;t` = (1/2)*Gr*(theta[i, j+1]+theta[i, j])+(1/2)*Gc*(C[i, j+1]+C[i, j])+(U[i-1, j+1]-2.*U[i, j+1]-2.*U[i, j]+U[i+1, j])/(2.*`&Delta;y`)^2-(1/2)*M*(U[i, j+1]+U[i, j]):

eq2[i, j] := (theta[i, j+1]-theta[i, j])/`&Delta;t` = (1/Pr)*(theta[i-1, j+1]-2*theta[i, j+1]+theta[i+1, j+1]+theta[i-1, j]-2*theta[i,j]+theta[i+1,j])/(2.*`&Delta;y`)^2-E*((1/`&Delta;y`)^2*(U[i+1, j]-U[i, j])^2):

eq3[i, j] := (C[i, j+1]-C[i, j])/`&Delta;t` = (1/Sc)*(C[i-1, j+1]-2*C[i, j+1]+C[i+1, j+1]+C[i-1, j]-2*C[i,j]+C[i+1,j])/(2*`&Delta;y`)^2-(K/2)*(C[i, j+1]-C[i, j]):
end do;  
Error, reserved word `end` unexpected
end do:
Error, reserved word `end` unexpected

# initial conditions
U[i, 0] := 0:
theta[i, 0]:= 0:
C[i, 0] := 0:
 

NULL;
U[0,j]:=exp(a*j*`&Delta;t`):
theta[0,j]:=(j*`&Delta;t`):
C[0,j]:=j*`&Delta;t`:

U[N,j]:=0:
theta[N,j]:=0:
C[N,j]:=0:

sys := ([seq])(seq(eq[i, j], j = 0 .. N), i = 1 .. N):
nops(sys);
vars:=indets(sys):
nn := Matrix(N+1, N+1,(i, j)-> U[i-1, j-1]):
##
p:=proc(kk) local U_res,A;
  U_res:=solve(eval(sys,k=kk),vars);
  A:=eval(nn,U_res);
  plots:-matrixplot(A)
end proc;

plots:-(U,[M],Y=0..4);

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I've found the Taylor series expansions for two functions.  The two expansions are identical until the third term.  When I subtract one expansion from the other, I expected that the identical terms would cancel and disappear.  But I can't get Maple to do this.  If I copy and paste the output into a Maple command, the "big Oh" terms are not treated correctly.  The correct answer would be (x^3)/6 + O(x^4).  Here's my work:
 

How can I get Maple to give me the right answer?  I tried various commands (collect, combine, simplify, etc.) but nothing worked.  Also, why do the font and color of my first two commands differ?  Thanks
 

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