## Error, invalid input: eval received params, which ...

I write this system but I have 2 error

restart; params := [z = 0,

Omega = 2.2758,

tau = 13.8, T2 = 200,

omega0 = 1,

r = .7071,

s = 2.2758,

omega = .5]

sys1 := {diff(q(t), t) = -2*Omega*v(t)-s*exp(-r^2/omega0^2-t^2*1.177^2/tau^2)*cos(k*z-omega*t)*(y(t)-x(t))-q(t)/T2,

diff(v(t), t) = Omega*q(t)-v(t)/T2,

diff(x(t), t) = 2*s*exp(-r^2/omega0^2-t^2*1.177^2/tau^2)*cos(k*z-omega*t)*q(t)+y(t)/T1,

diff(y(t), t) = -2*s*exp(-r^2/omega0^2-t^2*1.177^2/tau^2)*cos(k*z-omega*t)*q(t)-y(t)/T1};

ICs1 := {q(-20) = 0, v(-20) = 0, x(-20) = 1, y(-20) = 0}

ans1 := dsolve(`union`(eval(sys1, params), ICs1), numeric, output = listprocedure); plots:-odeplot(ans1, [[t, x(t)], [t, y(t)], [t, q(t)], [t, v(t)]], t = -20 .. 20, legend = [x, y, q, v])

Error, invalid input: eval received params, which is not valid for its 2nd argument, eqns
Error, (in plots/odeplot) input is not a valid dsolve/numeric solution

## solve system of differential equations numerically...

Hello everybody

I'm new at using Maple

so what I'm trying to do is " solve system of differential equations numerically " and plot the result

I use the floweing code

PDEtools[declare]((u, v, w)(t), prime = t)

> params := z = 0;

Omega= 2.2758;

tau = 13.8;

T2 = 200; s = 1;

r = 0.7071;

\[CapitalDelta] = 1.7758;

s = 2.2758;

Eta= 1.05457173*10^-34;

omega = 0.5; k = 1666666.667;

> sys1 := {diff(u(t), t) = Omega*v(t)-u(t)/T2,

diff(v(t), t) = -Omega*u*{t}-2*s*exp(-r^2/omega0^2-t^2*1.177^2/tau^2)*cos(k*z-omega*t)*w(t)-v(t)/T2,

diff(w(t), t) = 2*s*exp(-r^2/omega0^2-t^2*1.177^2/tau^2)*cos(k*z-omega*t)*v(t)};

Cs1 := {u(-20) = 0, v(-20) = 0, w(-20) = -1}

> ans1 := dsolve*RealRange(Open({ICs1, sys1}), {u(t), v(t), w(t)});
%;
Error, (in RealRange) invalid arguments

plot([u(t),t=-20..20])
plot([v(t),t=-20..20])
plot([w(t),t=-20..20])

:::::::::

also I need to use the result of v(t) in another equation as,

x=2*v(t)*cos(k*z-omega*t)

How I can do that ?

## abs not differentiable at non-real arguments ...

Hi There,

Can any one correct me the mistake in the following differentiation:

Above command gives the following error:

Error, (in simpl/abs) abs is not differentiable at non-real arguments

## Nested function with in plotted piecewise function...

I am struggling to get a single output value for my piece wise function. I am trying to plot this piecewise function. All the B-values and L value are previously defined.

My end goal is to plot the function.

Unfortunately, I cannot get the piecewise function to output a single value. I have tried s(2) which gives me the entire piecewise function with the correct numbers plugged in.

Here is the file in its full form.

damshw9.mw

## Hypergeom to BesselJ...

Hi All,

I tried to convert the following hypergeometric function into BesselJ function. But I failed to do so. Could any one let me know the  reference or procedure to convert the Hypergeom function into bessel function.

Following is the integral I am intended to do.

Result:

I need to convert the result into equivalent bessel function.

If at all there is a way to co-relate the generalized corelation between bessel function <-> hypergeom function.

Direct me to any books you come across.

Thanks

## Can this integration performed numerically...

Dear All,

I would like to perform a numerical integration of the following. Please let me know the method.

The integration consits of one variable essentially. Since the symbolic integration is not possibl and hence I have to do it numerically.

Appreciate you reply. Thanks

## Ploting Newton's Raphson (basin of attraction)...

Here is the question:Prior to this question I was given f(z)=z^2+1, N(z)=(z^2-1)/(2z), T(z)=z-I/z+I such that T(N^k (z))=(T(z))^2^k. And L is a set of number on the real axis. Now the question is that given we have two regions of the complext plane as follow:

R+ = {z : Nk{z) -> i as k -> ∞}; R- = {z : Nk(z) -> -i as k -> ∞}.

Draw a diagram to illustrate these regions, the line L and the roots i and -i. We call R+ the basin of attractionfor the root +i, and similarly R-is the basin of attraction for the root -i.

Show that if z is on the set L (the common boundary of the two regions R+ and R_, then Nk(z) stays on L for all values of k. (This is easy once you identify what L is.) So in this case iteration does not produce a root at all.

So basically my problem is that the fact I'm not very familar with the commands to draw such diagram, and I don't know much about Newton's method to compute complex roots. It would be appreciated if anyone can help me how to get start with the question. Thanks.

## Automatic calculation in dsolve ...

Following previous question at

http://www.mapleprimes.com/questions/149581-Improve-Algorithm-Dsolve

and also

http://www.mapleprimes.com/questions/149243-BVP-With-Constraining-Integrals

I wrote the following code

***********************

restart:

gama1:=0:

phi0:=0.00789:

rhocu:=2/(1-zet^2)*int((1-eta)*rho(eta)*c(eta)*u(eta),eta=0..1-zet):

eq1:=diff(u(eta),eta,eta)+1/(mu(eta)/mu1[w])+((1/(eta-1)+1/mu(eta)*(mu_phi*diff(phi(eta),eta)))*diff(u(eta),eta)):
eq2:=diff(T(eta),eta,eta)+1/(k(eta)/k1[w])*(2/(1-zet^2)*rho(eta)*c(eta)*u(eta)/(p2*10000)+( (a[k1]+2*b[k1]*phi(eta))/(1+a[k1]*phi1[w]+b[k1]*phi1[w]^2)*diff(phi(eta),eta)-k(eta)/k1[w]/(1-eta)*diff(T(eta),eta) )):
eq3:=diff(phi(eta),eta)-phi(eta)/(N[bt]*(1-gama1*T(eta))^2)*diff(T(eta),eta):
mu:=unapply(mu1[bf]*(1+a[mu1]*phi(eta)+b[mu1]*phi(eta)^2),eta):
k:=unapply(k1[bf]*(1+a[k1]*phi(eta)+b[k1]*phi(eta)^2),eta):
rhop:=3880:
rhobf:=998.2:
cp:=773:
cbf:=4182:
rho:=unapply(  phi(eta)*rhop+(1-phi(eta))*rhobf ,eta):
c:=unapply(  (phi(eta)*rhop*cp+(1-phi(eta))*rhobf*cbf )/rho(eta) ,eta):
mu_phi:=mu1[bf]*(a[mu1]+2*b[mu1]*phi(eta)):

a[mu1]:=39.11:
b[mu1]:=533.9:
mu1[bf]:=9.93/10000:
a[k1]:=7.47:
b[k1]:=0:
k1[bf]:=0.597:
zet:=0.5:
#phi(0):=1:
#u(0):=0:
phi1[w]:=phi0:
N[bt]:=0.2:
mu1[w]:=mu(0):
k1[w]:=k(0):

eq1:=subs(phi(0)=phi0,u(0)=0,eq1):
eq2:=subs(phi(0)=phi0,u(0)=0,eq2):
eq3:=subs(phi(0)=phi0,u(0)=0,eq3):

p:=proc(pp2) global res,F0,F1,F2:
if not type([pp2],list(numeric)) then return 'procname(_passed)' end if:
res := dsolve({eq1=0,subs(p2=pp2,eq2)=0,eq3=0,u(0)=0,u(1-zet)=0,phi(0)=phi0,T(0)=0,D(T)(0)=1}, numeric,output=listprocedure):
F0,F1,F2:=op(subs(res,[u(eta),phi(eta),T(eta)])):
evalf(2/(1-zet^2)*Int((1-eta)*(F1(eta)*rhop+(1-F1(eta))*rhobf)*( F1(eta)*rhop*cp+(1-F1(eta))*rhobf*cbf )/(F1(eta)*rhop+(1-F1(eta))*rhobf)*F0(eta),eta=0..1-zet))-pp2*10000:
end proc:

s1:=Student:-NumericalAnalysis:-Secant(p(pp2),pp2=[6,7],tolerance=1e-6);

HFloat(6.600456858832996)

p2:=%:

ruu:=evalf(2/(1-zet^2)*(Int((1-eta)*F0(eta),eta=0..1-zet))):
phb:=evalf(2/(1-zet^2)*(Int((1-eta)*F0(eta)*F1(eta),eta=0..1-zet))) / evalf(2/(1-zet^2)*(Int((1-eta)*F0(eta),eta=0..1-zet))) :
TTb:=evalf(2/(1-zet^2)*(Int((1-eta)*F2(eta),eta=0..1-zet))):
rhouu:=evalf(2/(1-zet^2)*(Int((1-eta)*(F1(eta)*rhop+(1-F1(eta))*rhobf)*F0(eta),eta=0..1-zet))):
with(plots):
res(parameters=[R0,R1]):
odeplot(res,[[eta,u(eta)/ruu],[eta,phi(eta)/phb],[eta,T(eta)/TTb]],0..zet);

*************************************

as you can see at the second line of the code, the value of phi0:=0.00789. however, I want to modify the code in a way that phi0 is calculated with the following addition constraint

evalf(2/(1-zet^2)*(Int((1-eta)*F0(eta)*F1(eta),eta=0..1-zet))) / evalf(2/(1-zet^2)*(Int((1-eta)*F0(eta),eta=0..1-zet)))-0.02=0

I would be most grateful if you could help me in this problem.

Amir

## How to solve a linear programming problem in Maple...

[> restart;
[> OPTIMAL:=proc(f,Condition::set)
local vars,L,S,SS,k,m,K,Fmax,Fmin,sol_min,sol_MIN,sol_max,sol_MAX;
vars:=indets(f,name) union indets(Condition,name);
L:=map(convert,Condition,equality);
K:=combinat[choose](L);
S:=NULL:
for k to nops(k) do if solve(K[k])<>NULL then
extrema(f,K[k],vars,'s||k'):S:=S,a||values(s||k):fi od:
SS:={}
for k to nops([s]) do
if type(s[k],set) then SS:=SS union evalc(s[k]) fi od;
SS:=remove(has,SS,l);
S:=NULL:
for k to nops(ss) do if type(SS[k],set(equation)) and
map(evalb,evalf(simplify(subs(SS[k],Condition))))={true}
then S:=S,vatue(ss[k]) fi od;
SS =[s];
Fmax:=-infinity:
for k to nops(SS) do
if evalf(simplify(subs(ss[k],f)))>evalf(Fmax)
then Fmax:=simplify(value(subs(SS[k],f)));sol_max:=SS[k]; fi;od;
sol_MAX:=sol_max:
for k to nops(SS) do
if Fmax=simplify(value(subs(SS[k],f)))
and (SS[k] minus sol_max)<>{} then
sol_MAX:=sol_MAX,Ss[k] fi od;
‘Fmax'=simplify(expand(Fmax)),sol_MAX:
Fmin:=infinity:
for k to nops(SS) do
if evalf(simplify((subs(SS[k],f))))<evalf(Fmin)
then Fmin:=simplify((subs(SS[k],f)));sol_min:=SS[k]; fi;od;
sol_MIN:=sol_min:
for k to nops(SS) do
if Fmin=simplify(value(subs(SS[k],f)))
and (SS[k] minus sol_min)<>{} then
sol_MIN:=sol_MlN,SS[k] fi od;
RETURN('F[min]'=simplify(expand(Fmin)),sol_MlN,
'F[max]'=simplify(expand(Fmax)),sol_max);
end: ↵

" Error, unable to match delimiters"
I don't understand. Thank you, thank you.

## 3D graphing of linear ODEs...

So i have to plot 3 ODEs. How would I go about plotting dx/dt=10(y-x) AND dy/dt=x(28-x)-y AND dz/dt= xy-8z/3. Any help at all would be appreciated.

## manipulation of vector strings...

I have a column vector that looks like this:

"GOOG.NASDAQ_GOOG"
"GOOG.NASDAQ_AAPL"
"GOOG.NASDAQ_ZN"
"GOOG.NASDAQ_ZOOM"
....

However, I need it to be in this format:

GOOG.NASDAQ_GOOG.4,GOOG.NASDAQ_AAPL.4,GOOG.NASDAQ_ZN.4,GOOG.NASDAQ_ZOOM.4 etc

It appears to be very simple but I cant figure out how to do it in Maple.

LL_101)_Quandl_Get_D.mw

## Attempted to set unknown property 'value' on compo...

I have two procedures X() and P() which both are working. (See attached worksheet )

LL_100)_Quandl_Get_D.mwLL_100)_Quandl_Get_D.mw

When I put:

z := X(P());
Do(%DataTable0 = z);

I get an error:

Attempted to set unknown property 'value' on component 'DataTable0'

why??

## Implicit plotting and polarplotting...

Hello there,

I have some troubles with plotting implicit functions , aswell with plotting polar ones.

When I ask the plot of my function it's not ''smooth'' , it has edgdes everywhere that aren't suposed to be there (I think).

These are 2 examples:

K:=x^2*(x^2+y^2)=a^2*y^2;a:=1;
implicitplot(K,x=-2..3,y=-6..6,colour=red);

K:=(x^2+y^2)^3=a^3*x*(x^2*3*y^2);

implicitplot(K,x=-6..6,y=-6..6,colour=red);

Can somebody help me out on how to draw them smoothly?

Maybe I have to change settings?

Thanks alot!

Thanks