## Non-Linear System, fsolve fails to find a solution...

Non-Linear.mw

Hi, I have here a interesting non-linear system.

If I attempt to solve it using some specific form of the non-linear equations (form X*Y=Z) of the system, Maple (Verison 18) finds a solution.

But, if I replace some of them by some other forms (like form Y=Z/X), fsolve fails.

I usually use the non-quotient form. But is there any way to guide or configure fsolve to reach a solution?
I set up some of the regular options: placing a seed close to the solution, indicating intervals of possible solutions; but none of that works if I do not set up the non-quotient form of the equations. In some cases, fsolve does not reach a solution at all, no matter the form of the equations.

In the file, the equations that are causing the isssue are the last 3, those who start with the variable f1,f2 and f3.
I ran the system twice with both cases: non-quotient form and quotient form.

## PDETools:-pdsolve other solutions...

Given a set (list) of PDE, is there a way to search all possible solution sets? For instance, pdsolve will output the solution

{_eta[0](t, x) = 0, _xi[t](t, x, u) = _C1, _xi[x](t, x, u) = _C2, eta[1](t, x) = 0}

for the list of PDEs below. But I am aware that there is another solution different from the above, is there way to seek these other solutions?

[alpha*u^2*(diff(eta[1](t, x), t))+alpha*u*(diff(_eta[0](t, x), t))-u*(diff(eta[1](t, x), t))-u*(diff(eta[1](t, x), x))+u*(diff(eta[1](t, x), x, x, t))-(diff(_eta[0](t, x), x))-(diff(_eta[0](t, x), t))+diff(_eta[0](t, x), x, x, t), -(diff(_xi[x](t, x, u), u, u, u)), -(diff(_xi[t](t, x, u), x))-(diff(_xi[t](t, x, u), t)), -(diff(_xi[t](t, x, u), x, x)), -2*(diff(_xi[t](t, x, u), x, x))-(diff(_xi[x](t, x, u), x, x))+2*(diff(eta[1](t, x), x)), diff(eta[1](t, x), t)-2*(diff(_xi[x](t, x, u), x, x)), -(diff(_xi[x](t, x, u), t))*alpha*u-(diff(_xi[x](t, x, u), x, x, x))-(diff(_xi[t](t, x, u), x))+2*(diff(eta[1](t, x), x, t)), -(diff(_xi[x](t, x, u), x)), -(diff(_xi[t](t, x, u), t))*alpha*u+(diff(_xi[t](t, x, u), x))*alpha*u+(diff(_xi[x](t, x, u), x))*alpha*u+(diff(_xi[x](t, x, u), t))*alpha*u+eta[1](t, x)*alpha*u+alpha*_eta[0](t, x)+diff(_xi[t](t, x, u), t)-(diff(_xi[t](t, x, u), x, x, x))-(diff(_xi[x](t, x, u), x))-(diff(_xi[x](t, x, u), t))+diff(eta[1](t, x), x, x), -2*(diff(_xi[x](t, x, u), u)), -2*(diff(_xi[t](t, x, u), x, u)), -2*(diff(_xi[t](t, x, u), u))-(diff(_xi[x](t, x, u), u)), -(diff(_xi[t](t, x, u), u)), -(diff(_xi[t](t, x, u), u)), -5*(diff(_xi[x](t, x, u), u, u)), -(diff(_xi[t](t, x, u), u, u)), -3*(diff(_xi[t](t, x, u), x, u)), -2*(diff(_xi[x](t, x, u), u)), -(diff(_xi[t](t, x, u), u)), -(diff(_xi[t](t, x, u), u)), -2*(diff(_xi[t](t, x, u), u, u))-(diff(_xi[x](t, x, u), u, u)), -(diff(_xi[t](t, x, u), u, u, u)), -3*(diff(_xi[t](t, x, u), u, u)), -3*(diff(_xi[t](t, x, u), x, u, u)), (diff(_xi[t](t, x, u), u))*alpha*u-(diff(_xi[x](t, x, u), u))-3*(diff(_xi[t](t, x, u), x, x, u)), -2*(diff(_xi[x](t, x, u), x, u))-4*(diff(_xi[t](t, x, u), x, u)), -(diff(_xi[t](t, x, u), u))*alpha*u+(diff(_xi[x](t, x, u), u))*alpha*u+diff(_xi[t](t, x, u), u)-(diff(_xi[x](t, x, u), u)), -3*(diff(_xi[x](t, x, u), x, x, u))-(diff(_xi[t](t, x, u), u)), -7*(diff(_xi[x](t, x, u), x, u)), -3*(diff(_xi[x](t, x, u), x, u, u))]

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 (2)
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 (4)
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 (5)
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 (6)
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 (7)
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 (8)
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## limit and series...

Why solutions (5) and (6) are different? The solution (5) is obtained by putting f=0 of the series, while (6) is the result by taking limit at f->0.

check.mw

## how do i calculate this integral...

hallo evert body please how i do calculate this integral

in maple 18

ttp.pdf

int_{0}^{2\pi}(\cos^{i}(\theta)-\cos^{i+2}(\theta))d\theta


## How to separate a maths function from a maple expr...

Please I will like to know if there exists any command to isolate the known regular mathematical functions from an expression. For example, given the equation

I need a means of isolating (ex & sin(v)) from the above expression

Thanks

## export image with minimum size...

How can we export image with minimum size? I plot the solution and then export the image as an .eps file. But when I try to generate the generate the pdf file on Latex, the file size is too large. But when I plot the solutions on Matlab and export the images as .eps file, then Latex generate pdf file with samll size. Why Maple generate images of large sizes?

solution.mw

## Maple Calculus Study Guide displays in Maple notat...

I am using the Calculus Study Guide and the mathematical notation is half Maple notation and then half typeset notation. I have tried to tweak with Tools>Options>Display settings but it stays the same

For example:

{a[n]}[n = n[0]]^infinity;, where
"a[n]"

is the general term for the sequence, and
"n[0]"

is the starting index.
The notation is often shortened to {a[n]}; to save printing costs.

...and the math notation past the word "where" is in typeset notation but changed to Maple Notation when I cut and pasted.

## How to use sequence in a procedure...

Please how can I define two sequences in a procedure with two arguments?

ans:= Array([seq( [j, doCalc(j, u)], j=-2..0, 0.006, u=1..334)]):

The procedure is doCalc(j,u)  and I received this error: invalid input: seq expects between 1 and 3 arguments, but received 4

Find attached my complete code.Seq_Proc.mw

## How to replace a row of a matrix with the row of a...

How to replace 7th-row(second last) of the matrix H116 (see eq. (14)) with the 1st-row of the matrix H16 (see eq. (15)) and create a new matrix of size same as H116?

matrixop.mw

## Variables in procedures....

Hi! Can anyone show me a quick example of a procedure with local and global variables?!? It seems that i'm not getting the hang of it, because i keep receiving "unable to parse" messages.

## During evaluating function...

During evaluating psi0 (see eq, (7))why we need two values of f (i.e., f,0 and f,3)? I asked one of my seniors and according to him these values are arbitrary. Can anyone explain why we need two values and why f,0 and f,3?

## HPM error with different do and end loop for same...

Dear maple user,

I have codes for Differential equations while applying one do and end loop i am able to plot the graph of G(x) while same problem with other way of applying do and end loop i am unable to plot. whats wrong with do and end loop. These are codes available in maple primes . while combining i am unable to plot .

any one resolve it.

restart:
with(DETools):
with(plots):
with(IntegrationTools):
de0 := {
(1-p)*(diff(f(x),x,x,x))+p*(diff(f(x),x,x,x)+(1/2)*f(x)*(diff(f(x),x,x))),
(1-p)*(diff(g(x),x$2))/Pr+p*((diff(g(x),x$2))/Pr+(1/2)*f(x)*(diff(g(x),x)))}:

ibvc0 := {f(0),(D(f))(0),(D(f))(5)-1,g(0)-1,g(5)}:
n:=2:

F := unapply( add(b[k](x)*p^k,k=0..n), x ):
G := unapply( add(c[k](x)*p^k,k=0..n), x ):

de := map( series, eval( de0, {f=F,g=G} ), p=0, n+1 ):

for k from 0 to n do

if k = 0 then
ibvc := expand( eval[recurse]( ibvc0, {f=F,g=G,p=0} ) ):
else
ibvc := { b[k](0), D(b[k])(0), (D@@2)(b[k])(0), c[k](0), D(c[k])(0) }:
end if:

sys := simplify( map( coeff, de, p, k ) ) union ibvc:
soln := dsolve( sys ):

b[k] := unapply( eval( b[k](x), soln ), x ):
c[k] := unapply( eval( c[k](x), soln ), x ):

end do:

'F(x)' = F(x)+O(p^(n+1)):
'G(x)' = G(x)+O(p^(n+1)):

Pr:=1:
plot(eval(G(x), p = 1), x = 0 .. 5, color = blue):
###### Same problem with other  way of do and and end loop unable to plot with G(x)
restart:
with(DETools):
with(plots):
with(IntegrationTools):
Pr:=1:
de1 := (1-p)*(diff(f(x), $(x, 3)))+p*(diff(f(x), $(x, 3))+(1/2)*f(x)*(diff(f(x), $(x, 2)))); de2 := (1-p)*(diff(g(x), $(x, 2)))/Pr+p*((diff(g(x), \$(x, 2)))/Pr+(1/2)*f(x)*(diff(g(x), x)));
ibvc := f(0), (D(f))(0), (D(f))(5)-1, g(0)-1, g(5); n := 2; F := unapply(add(b[k](x)*p^k, k = 0 .. n), x); G := unapply(add(c[k](x)*p^k, k = 0 .. n), x);
DE1 := series(eval(de1, f = F), p = 0, n+1);
DE2 := series(eval(de2, g = G), p = 0, n+1);
CO := map(coeffs, eval([ibvc], f = F), p); CT := map(coeffs, eval([ibvc], g = G), p);

for k from 0 to n do IBVC1 := select(has, C*T, c[k]); slv := dsolve({coeff(DE2, p, k), op(IBVC1)}); c[k] := unapply(rhs(slv), x) end do;
G(x) = G(x)+O(p^(n+1));
plot(eval(G(x), p = 1), x = 0 .. 5);

## How to rectify the "Error, invalid subscript selec...

Hi, Maple users

I hope you are doing well.
Here I solved one of the ode problems by dsolve.
But I am getting  "Error, invalid subscript selector" error.
Kindly do the needful to find a solution.
Thank you.

JVB.mw