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Hi guys! 

I have a PDE system. The mayority of the equations are equal to zero, but two of them are:

 

where a, b, c, d are CONSTANT parameters. I know that if a=b=d=c=1 the system is inconsistent. But I also know that if a=-1, b=d=0 and c=1 the system is consistent and exist the solution. I wanna know if there's a way to ask maple to find another selections of my parameter that make my PDE consistent and what it's the solution for that selection of a,b,c,d. 

Here's my PDE system (sys2). 

test.mw

thank you so much for your time! 

I understand that if I want to use a scientific constant in a Maple worksheet or document, I first have to declare it. Here is an example for the speed of light:

However if this worksheet is re-executed (e.g. using !!!) this happens:

Obviously there is a kind of recursion for c which is listed in the Variable Palette as a name for a variable but which is also the scientific constant. The problem can be solved e.g. by associating another name to the constant and unassigning the old definition in the Variable Palette:

This works but it makes the document harder to read since everybody is used to lowercase c for the speed of light. The same is of course true for other scientific constants.

Is there a way to use scientific constants in their "usual" notation in Maple, including using the unit of the constant?

I want to ask., I put delta as my constant in maple program and I want the answer are in delta as well., but the thing is., when running., it let delta=0, delta=-1, and delta=delta.,
the condition is we cannot let delta=1 or delta=0 because it is just same for s5 and s7.,.(delta is refer to the s8). How can I get answer as delta? with the condition? here I attach my maple programme..

 

> derivation := proc (A, n)
local i, j, k, t, s5, s7, s8, m, D,
sols5, sols7, sols8, eqns5, eqns7, eqns8,
BChange5, BChange7, BChange8; eqns5 := {}; eqns7 := {}; eqns8 := {};
D := matrix(n, n);
BChange5 := matrix(n, n); BChange7 := matrix(n, n); BChange8 := matrix(n, n);
for i to n do for j to n do for m to n do
s5 := sum(0*A[i, j, k]*D[m, k], k = 1 .. n)-(sum(A[k, j, m]*D[k, i]+A[i, k, m]*D[k, j], k = 1 .. n));
s7 := sum(0*A[i, j, k]*D[m, k], k = 1 .. n)-(sum(A[k, j, m]*D[k, i]+0*A[i, k, m]*D[k, j], k = 1 .. n));
s8 := sum(0*A[i, j, k]*D[m, k], k = 1 .. n)-(sum(A[k, j, m]*D[k, i]+delta*A[i, k, m]*D[k, j], k = 1 .. n));
eqns5 := `union`(eqns5, {s5}); eqns7 := `union`(eqns7, {s7}); eqns8 := `union`(eqns8, {s8})
end do end do end do;
sols5 := [solve(eqns5)]; sols7 := [solve(eqns7)]; sols8 := [solve(eqns8)];
t := nops(sols5); t := nops(sols7); t := nops(sols8);
for i to t do for j to n do for k to n do
BChange5[k, j] := subs(sols5[i], D[k, j]);
BChange7[k, j] := subs(sols7[i], D[k, j]);
BChange8[k, j] := subs(sols8[i], D[k, j])
end do end do;
print("eqns≔", eqns5); print("sols:=", sols5); print("BChange5:=", BChange5);
print("eqns≔", eqns7); print("sols:=", sols7); print("BChange8:=", BChange7);
print("eqns≔", eqns8); print("sols:=", sols8); print("BChange8:=", BChange8)
end do end proc;

> AS1 := array(sparse, 1 .. 2, 1 .. 2, 1 .. 2, [(1, 1, 2) = 1]);
> derivation(AS1, 2);

> AS2 := array(sparse, 1 .. 2, 1 .. 2, 1 .. 2, [(1, 1, 1) = 1, (1, 2, 2) = 1]);
> derivation(AS2, 2);

> AS3 := array(sparse, 1 .. 2, 1 .. 2, 1 .. 2, [(1, 1, 1) = 1, (2, 1, 2) = 1]);
> derivation(AS3, 2);

> AS4 := array(sparse, 1 .. 2, 1 .. 2, 1 .. 2, [(1, 1, 1) = 1, (2, 2, 2) = 1]);
> derivation(AS4, 2);

> AS5 := array(sparse, 1 .. 2, 1 .. 2, 1 .. 2, [(1, 1, 1) = 1, (1, 2, 2) = 1, (2, 1, 2) = 1]);
> derivation(AS5, 2);

> AS1 := array(sparse, 1 .. 3, 1 .. 3, 1 .. 3, [(1, 3, 2) = 1, (3, 1, 2) = 1]);
> derivation(AS1, 3);

> AS2 := array(sparse, 1 .. 3, 1 .. 3, 1 .. 3, [(1, 3, 2) = 1, (3, 1, 2) = alpha]);
> derivation(AS2, 3);

> AS3 := array(sparse, 1 .. 3, 1 .. 3, 1 .. 3, [(1, 1, 2) = 1, (1, 2, 3) = 1, (2, 1, 3) = 1]);
> derivation(AS3, 3);

> AS4 := array(sparse, 1 .. 3, 1 .. 3, 1 .. 3, [(1, 3, 2) = 1, (2, 3, 2) = 1, (3, 3, 3) = 1]);
> derivation(AS4, 3);

> AS5 := array(sparse, 1 .. 3, 1 .. 3, 1 .. 3, [(2, 3, 2) = 1, (3, 1, 1) = 1, (3, 3, 3) = 1]);
> derivation(AS5, 3);

> AS6 := array(sparse, 1 .. 3, 1 .. 3, 1 .. 3, [(3, 1, 2) = 1, (3, 2, 2) = 1, (3, 3, 3) = 1]);
> derivation(AS6, 3);

> AS7 := array(sparse, 1 .. 3, 1 .. 3, 1 .. 3, [(1, 2, 1) = 1, (2, 2, 2) = 1, (3, 1, 1) = 1, (3, 3, 3) = 1]);
> derivation(AS7, 3);

> AS8 := array(sparse, 1 .. 3, 1 .. 3, 1 .. 3, [(1, 3, 1) = 1, (2, 3, 2) = 1, (3, 1, 1) = 1, (3, 3, 3) = 1]);
> derivation(AS8, 3);

> AS9 := array(sparse, 1 .. 3, 1 .. 3, 1 .. 3, [(2, 3, 2) = 1, (3, 1, 1) = 1, (3, 2, 2) = 1, (3, 3, 3) = 1]);
> derivation(AS9, 3);

> AS10 := array(sparse, 1 .. 3, 1 .. 3, 1 .. 3, [(1, 3, 1) = 1, (2, 3, 2) = 1, (3, 1, 1) = 1, (3, 2, 2) = 1, (3, 3, 3) = 1]);
> derivation(AS10, 3);

> AS11 := array(sparse, 1 .. 3, 1 .. 3, 1 .. 3, [(1, 3, 2) = 1, (2, 3, 2) = 1, (3, 1, 2) = 1, (3, 2, 2) = 1, (3, 3, 3) = 1]);
> derivation(AS11, 3);

> AS12 := array(sparse, 1 .. 3, 1 .. 3, 1 .. 3, [(1, 1, 2) = 1, (1, 3, 1) = 1, (2, 3, 2) = 1, (3, 1, 1) = 1, (3, 2, 2) = 1, (3, 3, 3) = 1]);
> derivation(AS12, 3);

> AS13 := array(sparse, 1 .. 3, 1 .. 3, 1 .. 3, [(1, 1, 1) = 1, (2, 2, 2) = 1, (3, 3, 3) = 1]);
> derivation(AS13, 3);

> AS14 := array(sparse, 1 .. 3, 1 .. 3, 1 .. 3, [(1, 2, 1) = 1, (2, 1, 1) = 1, (2, 2, 2) = 1, (3, 3, 3) = 1]);
> derivation(AS14, 3);

> AS15 := array(sparse, 1 .. 3, 1 .. 3, 1 .. 3, [(1, 2, 1) = 1, (2, 2, 2) = 1, (3, 3, 3) = 1]);
> derivation(AS15, 3);

> AS16 := array(sparse, 1 .. 3, 1 .. 3, 1 .. 3, [(2, 1, 1) = 1, (2, 2, 2) = 1, (3, 3, 3) = 1]);
> derivation(AS16, 3);

> AS17 := array(sparse, 1 .. 3, 1 .. 3, 1 .. 3, [(1, 1, 2) = 1, (3, 3, 3) = 1]);
> derivation(AS17, 3);
>

When solving ODE with dsolve, I don't want to use "_C1" as the name of constant, I want to specify by myself, how can I do?

Hi

Anyone could help me in solving the following system of equations to get constants C1, C2, C3 and C4. MALPE give me this "soution may have been lost".  The MAPLE sheet is also attached.

 

restart:

Eq1:=simplify(C3*exp(-(1/4)*(C2*(x^2-2*0)+sqrt(C2*(x^2-2*0)^2+4*M*(x^2-2*0)*w1*(x^2-2*0)))/w1)+C4*exp((1/4)*(-C2*(x^2-2*0)+sqrt(C2*(x^2-2*0)^2+4*M*(x^2-2*0)*w1*(x^2-2*0)))/w1)-U) = 0;

C3*exp(-(1/4)*(C2*x^2+(x^4*(4*M*w1+C2))^(1/2))/w1)+C4*exp(-(1/4)*(C2*x^2-(x^4*(4*M*w1+C2))^(1/2))/w1)-U = 0

(1)

Eq2:=simplify(exp(-(1/4)*(C2+sqrt(C2^2+4*M*w1))*(x^2-2*0)/w1)*C3*x+exp((1/4)*(-C2+sqrt(C2^2+4*M*w1))*(x^2-2*0)/w1)*C4*x+C2-V-z) = 0;

exp(-(1/4)*(C2+(C2^2+4*M*w1)^(1/2))*x^2/w1)*C3*x+exp(-(1/4)*(C2-(C2^2+4*M*w1)^(1/2))*x^2/w1)*C4*x+C2-V-z = 0

(2)

Eq3:=simplify((-2*w2*w5*ln(C3*exp(-(1/2)*sqrt(w2*w4*(w2*w4+w3*w6))*C2*(x^2-2*0)/(w2*w4*w5))-C4)*sqrt(w2*w4*(w2*w4+w3*w6))+w2*w5*(-w2*w4+sqrt(w2*w4*(w2*w4+w3*w6)))*ln(exp(-(1/2)*sqrt(w2*w4*(w2*w4+w3*w6))*C2*(x^2-2*0)/(w2*w4*w5)))+C1*w3*w6*sqrt(w2*w4*(w2*w4+w3*w6)))/(sqrt(w2*w4*(w2*w4+w3*w6))*w3*w6)-1)= 0;

(-ln(exp(-(1/2)*(w2*w4*(w2*w4+w3*w6))^(1/2)*C2*x^2/(w2*w4*w5)))*w2^2*w4*w5+C1*w3*w6*(w2*w4*(w2*w4+w3*w6))^(1/2)-2*w2*w5*ln(C3*exp(-(1/2)*(w2*w4*(w2*w4+w3*w6))^(1/2)*C2*x^2/(w2*w4*w5))-C4)*(w2*w4*(w2*w4+w3*w6))^(1/2)+ln(exp(-(1/2)*(w2*w4*(w2*w4+w3*w6))^(1/2)*C2*x^2/(w2*w4*w5)))*(w2*w4*(w2*w4+w3*w6))^(1/2)*w2*w5-(w2*w4*(w2*w4+w3*w6))^(1/2)*w3*w6)/((w2*w4*(w2*w4+w3*w6))^(1/2)*w3*w6) = 0

(3)

Eq4:= simplify((-C2*x^2*w2*w4-.50*C2*x^2*w3*w6+sqrt(w2*w4*(w2*w4+w3*w6))*C2*x^2+2.*w2*w4*w5*ln(w3^4*w6^2*(C3^2*exp(-1.0*sqrt(w2*w4*(w2*w4+w3*w6))*C2*x^2/(w2*w4*w5))-2*C3*exp(-.5*sqrt(w2^2*w4^2+w2*w3*w4*w6)*C2*x^2/(w2*w4*w5))*C4+C4^2)/(w2*w4*(w2*w4+w3*w6)*C2^2))-5.544000000*w2*w4*w5-w3^2*w6)/(w3^2*w6)) = 0;

(-C2*x^2*w2*w4-.5000000000*C2*x^2*w3*w6+(w2*w4*(w2*w4+w3*w6))^(1/2)*C2*x^2+2.*w2*w4*w5*ln(w3^4*w6^2*(C3^2*exp(-(w2*w4*(w2*w4+w3*w6))^(1/2)*C2*x^2/(w2*w4*w5))-2.*C3*exp(-.5*(w2*w4*(w2*w4+w3*w6))^(1/2)*C2*x^2/(w2*w4*w5))*C4+C4^2)/(w2*w4*(w2*w4+w3*w6)*C2^2))-5.544000000*w2*w4*w5-w3^2*w6)/(w3^2*w6) = 0

(4)

solve({Eq1, Eq2, Eq3,Eq4}, {C1, C2, C3,C4});

Warning, solutions may have been lost

 

``

``

Download solution_lost.mw

 

 

There is an heuristic-free algorithm, designed by Greg Reid to find structure constant of finite dimension Lie algebra of symmetries, admitted by differential equation. Details could be found in his paper:

http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=2316480

 

The main problem - I couldn't find implementation of it in Maple...

Hi all

How can I construct following triangular block matrix?

where

and

P is (N*M)*(N*M) and E and H are M*M matrices. tf is known constant.

thanks in advance

 

Mahmood   Dadkhah

Ph.D Candidate

Applied Mathematics Department

For all real a, the partial sums sn= sum((-1)^k (k^(1/k) -a), k=1..n) are bounded so that their limit points form an interval [-1.+  the MRB constant +a, MRB constant] of length 1-a, where the MRB constant is limit(sum((-1)^k*(k^(1/k)), k = 1 ..2*N),N=infinity).

For all complex z, the upper limit point of  sn= sum((-1)^k (k^(1/k) -z), k=1..n) is the  the MRB constant.

We see that maple knows the basics of this because when we enter sum((-1)^k*(k^(1/k)-z), k = 1 .. n) 

maple gives

sum((-1)^k*(k^(1/k)-z), k = 1 .. n)

 

marvinrayburns.com

I have some data for a model in MapleSim that I would like to use a time look up table with.  I've found that the two options for interpolation are linear and 1st derivative, but the data was intended to be interpretted as piecewise constant.  Is there any way to acheive this option in MapleSim?

Hello guys ...

I used a numerically method to solve couple differential equation that it has some boundary conditions. My problem is that some range of answers has 50% error . Do you know things for improving our answers in maple ?

my problem is :

a*Φ''''(x)+b*Φ''(x)+c*Φ(x)+d*Ψ''(x)+e*Ψ(x):=0

d*Φ''(x)+e*Φ(x)+j*Ψ''(x)+h*Ψ(x):=0

suggestion method by preben Alsholm:

a,b,c,d,e,j,h are constants.suppose some numbers for these constants . I used this code:


VR22:=0.1178*diff(phi(x),x,x,x,x)-0.2167*diff(phi(x),x,x)+0.0156*diff(psi(x),x,x)+0.2852*phi(x)+0.0804*psi(x);
VS22:=0.3668*diff(psi(x),x,x)-0.0156*diff(phi(x),x,x)-0.8043*psi(x)-0.80400*phi(x);
bok:=evalf(dsolve({VR22=0,VS22=0}));

PHI,PSI:=op(subs(bok,[phi(x),psi(x)]));
Eqs:={eval(PHI,x=1.366)=1,eval(diff(PHI,x),x=1.366)=0,eval(PHI,x=-1.366)=1,eval(diff(PHI,x),x=-1.366)=0,
eval(PSI,x=1.366)=1,eval(PSI,x=1.366)=1};
C:=fsolve(Eqs,indets(%,name));
eval(bok,C);
SOL:=fnormal(evalc(%));


I used digits for my code at the first of writting.

please help me ... what should i do?

Hello.

 

Could not evaluate numerical integral with constant in it. I use method = _cuhre.  Maple print solution like this:

 

Int(Int(Int(max(0., (0.9483573506e-3*(-1.*sin(a)*cos(w)-1.*cos(a)*sin(w)*sin(b)))*cos(a)*cos(b)^2*(-58.5*signum(cos(b)*sin(w)*sin(b))*kk+200.*cos(b)*sin(w)*sin(b))*Heaviside(-58.5+200.*cos(b)*sin(w)*sin(b)*signum(cos(b)*sin(w)*sin(b))*kk)*Heaviside(1.-.98*cos(b)^2)/sqrt(1.-.98*cos(b)^2)), a = 0. .. 6.283185308), b = 0. .. 1.570796327), w = 0. .. 6.283185308)+Int(Int(Int(min(0., (0.9483573506e-3*(-1.*sin(a)*cos(w)-1.*cos(a)*sin(w)*sin(b)))*cos(a)*cos(b)^2*(-58.5*signum(cos(b)*sin(w)*sin(b))*kk+200.*cos(b)*sin(w)*sin(b))*Heaviside(-58.5+200.*cos(b)*sin(w)*sin(b)*signum(cos(b)*sin(w)*sin(b))*kk)*Heaviside(1.-.98*cos(b)^2)/sqrt(1.-.98*cos(b)^2)), a = 0. .. 6.283185308), b = 0. .. 1.570796327), w = 0. .. 6.283185308)

How could it be taken.

Thank!!!

 

Hi!

Say, I got an expression that depends on two variables, x and y. How can I tell Maple, that y is actually just a (real) constant, so y does not depend on x?

Because when I apply a differentiation with the "D" - command, it would always also write out expressions, where y is differentiated w.r.t. x.

Thanks!

Hey, I have a system of ODE and I can't draw it's phase curve. I tried to use DEplot and phaseportrait, but it doesn't work. Here is my system:

 dx/dt=x

dy/dt=ky              (k is a constant)

 

Here is my piece of code:

DE := [diff(x(t), t) = x(t)];

DF := [diff(y(t), t) = k*y(t)];

with(DEtools);

phaseportrait([DE, DF], [y, x], t = -5 .. 5, y = -5 .. 5, x = -5 .. 5, k...

Hello, I have a problem with plotting graphs with a constant.. I have one system of equations and one another equation:

dx/dt=x(t)

dy/dt=ky(t)

and 

|y|=C|x|^k

 

I need to compare theit curves.

k and C are constants. I thought it is alright if I would remove constants, BUT there is one in the power, so I have no idea what to do.. 

I just tried to plot the system, but it doesn't work either:

Thanks a lot Markiyan, and I am sorry I may have overlooked this already answered question. But, now I have just one more thing to know. On using AllSolutions = true in solve I get the answer as x = _z1~ ∏ / k, I then try to subs my fav symbol N instead of _Z1~, but Maple doesn't take it! It keeps it as it is. What kind of constant is this _Z1~, I had thought it to be the same as _C1, which is used by Maple while solving any ODE.

Reason why I want to...

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