Maple 12 Questions and Posts

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Hi,

how can I solve a set of first order, coupled, non-linear and inhomogeneous differential equations using MAPLE 12.

How can I solve a differential equation set of the type,

dy(x)/dx +y^2 =P(x); dP(x)/dx = R(P) numerically

How can I plot multiple numeric plots, such that numeric solutions belong to different differential equations?

Hai everyone. I used maple 12 and have an equation as follow:

int(int(lambda[v]*lambda[t]*exp(-lambda[v]*v-lambda[t]*t), v = (1/2)*(q[p]+q[p]*t[c]*t+2*S[di]*h*t)/(h*t) .. infinity), t = 0 .. infinity)

 

and try to get an outcome as follow:

However, I cannot get the outcome like I want. The maple just diplay the equation. Any tips or suggestion?

Thanks

Regards,

Dolby87

Hello,

can I remove tick marks from axis in plots ?

i want to find initial condition for F(0),G(0), H(0) and thetap(0) which is are missing in this problem.. then i facing this error Error, (in dsolve/numeric/bvp) Newton iteration is not converging



Maple Worksheet - Error

Failed to load the worksheet /maplenet/convert/hydronew2.mw .

Download hydronew2.mw

i am trying to solve 6 ODE with boundary condition


restart

with*plots

with*plots

(1)

Eq1 := (1-theta(eta)/theta[r])*(diff(f(eta), eta, eta, eta))+(diff(f(eta), eta, eta))*(diff(theta(eta), eta))/theta[r]+(1-theta(eta)/theta[r])^2*(f(eta)*(diff(f(eta), eta, eta))-(diff(f(eta), eta))^2-M*(diff(f(eta), eta))+B*H(eta)*(F(eta)-(diff(f(eta), eta)))) = 0

(1-theta(eta)/theta[r])*(diff(diff(diff(f(eta), eta), eta), eta))+(diff(diff(f(eta), eta), eta))*(diff(theta(eta), eta))/theta[r]+(1-theta(eta)/theta[r])^2*(f(eta)*(diff(diff(f(eta), eta), eta))-(diff(f(eta), eta))^2-M*(diff(f(eta), eta))+B*H(eta)*(F(eta)-(diff(f(eta), eta)))) = 0

(2)

Eq2 := G(eta)*(diff(F(eta), eta))+F(eta)^2+B*(F(eta)-(diff(f(eta), eta))) = 0

G(eta)*(diff(F(eta), eta))+F(eta)^2+B*(F(eta)-(diff(f(eta), eta))) = 0

(3)

Eq3 := G(eta)*(diff(G(eta), eta))+B*(f(eta)+G(eta)) = 0

G(eta)*(diff(G(eta), eta))+B*(f(eta)+G(eta)) = 0

(4)

Eq4 := G(eta)*(diff(H(eta), eta))+H(eta)*(diff(G(eta), eta))+F(eta)*H(eta) = 0

G(eta)*(diff(H(eta), eta))+H(eta)*(diff(G(eta), eta))+F(eta)*H(eta) = 0

(5)

Eq5 := (1+s*theta(eta))*(diff(theta(eta), eta, eta))+(diff(theta(eta), eta))^2*s+Pr*(f(eta)*(diff(theta(eta), eta))-(diff(f(eta), eta))*theta(eta))+(2/3)*B*H(eta)*(theta[p](eta)-theta(eta)) = 0

(1+s*theta(eta))*(diff(diff(theta(eta), eta), eta))+(diff(theta(eta), eta))^2*s+Pr*(f(eta)*(diff(theta(eta), eta))-(diff(f(eta), eta))*theta(eta))+(2/3)*B*H(eta)*(theta[p](eta)-theta(eta)) = 0

(6)

Eq6 := 2*F(eta)*theta[p](eta)+G(eta)*(diff(theta[p](eta), eta))+L0*B*(theta[p](eta)-theta(eta)) = 0

2*F(eta)*theta[p](eta)+G(eta)*(diff(theta[p](eta), eta))+L0*B*(theta[p](eta)-theta(eta)) = 0

(7)

bcs1 := f(0) = 0, (D(f))(0) = 1, (D(f))(10) = 0;

f(0) = 0, (D(f))(0) = 1, (D(f))(10) = 0

(8)

fixedparameter := [M = .5, B = .5, theta[r] = -10, L0 = 1, s = .1, Pr = 1];

[M = .5, B = .5, theta[r] = -10, L0 = 1, s = .1, Pr = 1]

(9)

Eq7 := eval(Eq1, fixedparameter);

(1+(1/10)*theta(eta))*(diff(diff(diff(f(eta), eta), eta), eta))-(1/10)*(diff(diff(f(eta), eta), eta))*(diff(theta(eta), eta))+(1+(1/10)*theta(eta))^2*(f(eta)*(diff(diff(f(eta), eta), eta))-(diff(f(eta), eta))^2-.5*(diff(f(eta), eta))+.5*H(eta)*(F(eta)-(diff(f(eta), eta)))) = 0

(10)

Eq8 := eval(Eq2, fixedparameter);

G(eta)*(diff(F(eta), eta))+F(eta)^2+.5*F(eta)-.5*(diff(f(eta), eta)) = 0

(11)

Eq9 := eval(Eq3, fixedparameter);

G(eta)*(diff(G(eta), eta))+.5*f(eta)+.5*G(eta) = 0

(12)

Eq10 := eval(Eq5, fixedparameter);

(1+.1*theta(eta))*(diff(diff(theta(eta), eta), eta))+.1*(diff(theta(eta), eta))^2+f(eta)*(diff(theta(eta), eta))-(diff(f(eta), eta))*theta(eta)+.3333333333*H(eta)*(theta[p](eta)-theta(eta)) = 0

(13)

Eq11 := eval(Eq6, fixedparameter);

2*F(eta)*theta[p](eta)+G(eta)*(diff(theta[p](eta), eta))+.5*theta[p](eta)-.5*theta(eta) = 0

(14)

bcs2 := F(10) = 0;

F(10) = 0

(15)

bcs3 := G(10) = -f(10);

G(10) = -f(10)

(16)

bcs4 := H(10) = n;

H(10) = n

(17)

bcs5 := theta(10) = 0;

theta(10) = 0

(18)

bcs6 := theta[p](10) = 0;

theta[p](10) = 0

(19)

L := [.2];

[.2]

(20)

for k to 1 do R := dsolve(eval({Eq10, Eq11, Eq4, Eq7, Eq8, Eq9, bcs1, bcs2, bcs3, bcs4, bcs5, bcs6}, n = L[k]), [f(eta), F(eta), G(eta), H(eta), theta(eta), theta[p](eta)], numeric, output = listprocedure); Y || k := rhs(R[5]); YP || k := rhs(R[6]); YJ || k := rhs(R[7]); YS || k := rhs(R[2]) end do

``


Download hydro.mw

restart

with*plots

with*plots

(1)

Eq1 := (1-theta(eta)/theta[r])*(diff(f(eta), eta, eta, eta))+(diff(f(eta), eta, eta))*(diff(theta(eta), eta))/theta[r]+(1-theta(eta)/theta[r])^2*(f(eta)*(diff(f(eta), eta, eta))-(diff(f(eta), eta))^2-M*(diff(f(eta), eta))+B*H(eta)*(F(eta)-(diff(f(eta), eta)))) = 0

(1-theta(eta)/theta[r])*(diff(diff(diff(f(eta), eta), eta), eta))+(diff(diff(f(eta), eta), eta))*(diff(theta(eta), eta))/theta[r]+(1-theta(eta)/theta[r])^2*(f(eta)*(diff(diff(f(eta), eta), eta))-(diff(f(eta), eta))^2-M*(diff(f(eta), eta))+B*H(eta)*(F(eta)-(diff(f(eta), eta)))) = 0

(2)

Eq2 := G(eta)*(diff(F(eta), eta))+F(eta)^2+B*(F(eta)-(diff(f(eta), eta))) = 0

G(eta)*(diff(F(eta), eta))+F(eta)^2+B*(F(eta)-(diff(f(eta), eta))) = 0

(3)

Eq3 := G(eta)*(diff(G(eta), eta))+B*(f(eta)+G(eta)) = 0

G(eta)*(diff(G(eta), eta))+B*(f(eta)+G(eta)) = 0

(4)

Eq4 := G(eta)*(diff(H(eta), eta))+H(eta)*(diff(G(eta), eta))+F(eta)*H(eta) = 0

G(eta)*(diff(H(eta), eta))+H(eta)*(diff(G(eta), eta))+F(eta)*H(eta) = 0

(5)

Eq5 := (1+s*theta(eta))*(diff(theta(eta), eta, eta))+(diff(theta(eta), eta))^2*s+Pr*(f(eta)*(diff(theta(eta), eta))-(diff(f(eta), eta))*theta(eta))+(2/3)*B*H(eta)*(theta[p](eta)-theta(eta)) = 0

(1+s*theta(eta))*(diff(diff(theta(eta), eta), eta))+(diff(theta(eta), eta))^2*s+Pr*(f(eta)*(diff(theta(eta), eta))-(diff(f(eta), eta))*theta(eta))+(2/3)*B*H(eta)*(theta[p](eta)-theta(eta)) = 0

(6)

Eq6 := 2*F(eta)*theta[p](eta)+G(eta)*(diff(theta[p](eta), eta))+L0*B*(theta[p](eta)-theta(eta)) = 0

2*F(eta)*theta[p](eta)+G(eta)*(diff(theta[p](eta), eta))+L0*B*(theta[p](eta)-theta(eta)) = 0

(7)

bcs1 := f(0) = 0, (D(f))(0) = 1, (D(f))(10) = 0;

f(0) = 0, (D(f))(0) = 1, (D(f))(10) = 0

(8)

fixedparameter := [M = .5, B = .5, theta[r] = -10, L0 = 1, s = .1, Pr = 1];

[M = .5, B = .5, theta[r] = -10, L0 = 1, s = .1, Pr = 1]

(9)

Eq7 := eval(Eq1, fixedparameter);

(1+(1/10)*theta(eta))*(diff(diff(diff(f(eta), eta), eta), eta))-(1/10)*(diff(diff(f(eta), eta), eta))*(diff(theta(eta), eta))+(1+(1/10)*theta(eta))^2*(f(eta)*(diff(diff(f(eta), eta), eta))-(diff(f(eta), eta))^2-.5*(diff(f(eta), eta))+.5*H(eta)*(F(eta)-(diff(f(eta), eta)))) = 0

(10)

Eq8 := eval(Eq2, fixedparameter);

G(eta)*(diff(F(eta), eta))+F(eta)^2+.5*F(eta)-.5*(diff(f(eta), eta)) = 0

(11)

Eq9 := eval(Eq3, fixedparameter);

G(eta)*(diff(G(eta), eta))+.5*f(eta)+.5*G(eta) = 0

(12)

Eq10 := eval(Eq5, fixedparameter);

(1+.1*theta(eta))*(diff(diff(theta(eta), eta), eta))+.1*(diff(theta(eta), eta))^2+f(eta)*(diff(theta(eta), eta))-(diff(f(eta), eta))*theta(eta)+.3333333333*H(eta)*(theta[p](eta)-theta(eta)) = 0

(13)

Eq11 := eval(Eq6, fixedparameter);

2*F(eta)*theta[p](eta)+G(eta)*(diff(theta[p](eta), eta))+.5*theta[p](eta)-.5*theta(eta) = 0

(14)

bcs2 := F(10) = 0;

F(10) = 0

(15)

bcs3 := G(10) = -f(10);

G(10) = -f(10)

(16)

bcs4 := H(10) = n;

H(10) = n

(17)

bcs5 := theta(10) = 0;

theta(10) = 0

(18)

bcs6 := theta[p](10) = 0;

theta[p](10) = 0

(19)

L := [.2];

[.2]

(20)

for k to 1 do R := dsolve(eval({Eq10, Eq11, Eq4, Eq7, Eq8, Eq9, bcs1, bcs2, bcs3, bcs4, bcs5, bcs6}, n = L[k]), [f(eta), F(eta), G(eta), H(eta), theta(eta), theta[p](eta)], numeric, output = listprocedure); Y || k := rhs(R[5]); YP || k := rhs(R[6]); YJ || k := rhs(R[7]); YS || k := rhs(R[2]) end do

``


then i get this error

Error, (in dsolve/numeric/bvp/convertsys) unable to convert to an explicit first-order system

i dont know where i need to change after view it one by one..

Download hydro.mw

i am solving 4 ODE with boundary condition..

> restart;
> with*plots;

 

then i got this error..

Error, (in dsolve/numeric/bvp/convertsys) unable to convert to an explicit first-order system

 

i dont know where i need to change.. could you help me..

 

 

 

I am getting a complex solution for a physical quantity, how can I plot it. Should I plot the real part or modulus?

solution is,

C1*sqrt(4*tau^2*M^2*lambda^2+Q^2)*LegendreP((1/2*I)*sqrt(7)-1/2, I*sqrt(7), (2*I)*lambda*M*tau/Q)+C2*sqrt(4*tau^2*M^2*lambda^2+Q^2)*LegendreQ((1/2*I)*sqrt(7)-1/2, I*sqrt(7), (2*I)*lambda*M*tau/Q)

 

where C1 and C2 are integration constants.

I'm trying to numerically calculate the following:

int(e^(-1.5*t)/sqrt(t*(t+1)), t = 1 .. infinity)

But Maple can't do it.

I then made it a lot simpler and tried to calculate the following:

evalf(int ((e^(-t)), t=1..infinity));

 

Thats just e^(-t), integrated from t=1 to t=infinity.

 

Maple just gives me back the original equation in the first case, and in the second gives me a limit that I can see has a numerical answer, but Maple can't. Is this something Maple should be able to do and I'm just now pushing the right buttons? I'm using Maple 12, which I know is old and limited, but these really aren't very complicated numerical integrations.

 

 

 

How can I get solution of  the following equation of orbit for schwarzschild BH in form of Jacobi Elliptical Integrals on Maple 12 platform,

diff(r(phi), phi) = r^2*sqrt(e^2-(1-2*M/r)*(1+l^2/r^2))/l

hello,

I'm trying to solve the equation of a form like,

diff(eta(tau), tau, tau)+(8/(4*tau^2+1)-32/(4*tau^2+1)^2)*eta(tau) = 0,

when I'm doing solve DE, I get a solution as:=

eta(tau) = _C1*sqrt(4*tau^2+1)*LegendreP((1/2*I)*sqrt(7)-1/2, I*sqrt(7), (2*I)*tau)+_C2*sqrt(4*tau^2+1)*LegendreQ((1/2*I)*sqrt(7)-1/2, I*sqrt(7), (2*I)*tau

which is combination of Legendre Polynomials with imaginary arguments,May I change this form,

How can I plot this solution on real plane, as this is imaginary,

Is the only option remaining NUMERIC PLOT??

How can I get and install grtensor for MAPLE12 on WIN7 32bit platform,

I tried with http://grtensor.phy.queensu.ca, downloaded grtii6.exe, now how to proceed further???

How can I calculate GR tensors and geodesic equations for adS schwarzschild spacetime.

How can I've shaded region with non-linear inequality, I have some potential function like V(r)=(1-2Me-2lr+q2e-4lr) and I want to shade area between this & x-axis,

when I'm doing it with inequlityplot, it says that inequality should be linear.

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