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Hi there,

I'm quite new to Maple so please forgive me! I have a system of partial differential equations I'm trying to solve in Maple as such below 

 

df/dt = f(1-f) - f * h

dg/dt = g(1-g) * Gradient(1-f * gradient(g))

dh/dt = (g - h) + Laplacian(h),

where f,g,h are functions of space and time (i.e. f(x,y,z,t)). I guess my first question is - is this possible in Maple to evaluate? (I'm currently unsure on ICs as I'm figuring it out from the model - it's a model for cancer growth I'm trying to evaluate but have a rough idea of what I'd use).

If it is possible, can you please share how I'd write this? Everytime I've tried I seem to be failing to define anything properly, so your expertise would be greatly appreciated!

I'm attempting to plot several solutions of this differential equation (I have uploaded my worksheet). I have used this series of commands before without issue, but for some reason I keep getting the error message: "Error, (in plot) incorrect first argument" ect.. Does anyone have any insight into what might be going wrong? Thank you.

Download ass_1_#9.mw

ass_1_#9.mw

restart;

diffeq := diff(w(r), `$`(r, 1))+2*beta*(diff(w(r), `$`(r, 1)))^3-(1/2)*S*(r-m^2/r) = 0;

con := w(1) = 1;

ODE := {con, diffeq};

sol := dsolve(ODE, w(r), type = numeric);

 

How can i have numerical solution of the above differential equation with corresponding boundary condition?

 

hi,

     there is a common  differential equation in my maple note,the solution of the eq. can be expressed by

associated Legendre function(s),but i get a result by hypergeometric representation.how i can translate the later into a  single Legendre fun?

 Thank you in advance  

ode := 'sin(theta)*(diff(sin(theta)*(diff(Theta(theta), theta)), theta))'/Theta(theta)+l*(l+1)*sin(theta)^2 = m^2

sin(theta)*(diff(sin(theta)*(diff(Theta(theta), theta)), theta))/Theta(theta)+l*(l+1)*sin(theta)^2 = m^2

(1)

dsolve(ode)

Theta(theta) = _C1*((1/2)*cos(2*theta)-1/2)^((1/2)*m)*sin(2*theta)*hypergeom([(1/2)*m+(1/2)*l+1, (1/2)*m-(1/2)*l+1/2], [3/2], (1/2)*cos(2*theta)+1/2)/(1-cos(2*theta))^(1/2)+_C2*hypergeom([(1/2)*m-(1/2)*l, (1/2)*m+(1/2)*l+1/2], [1/2], (1/2)*cos(2*theta)+1/2)*(-2*cos(2*theta)+2)^(1/2)*((1/2)*cos(2*theta)-1/2)^((1/2)*m)/(1-cos(2*theta))^(1/2)

(2)

`assuming`([simplify(dsolve(ode))], [l::posint, m::integer, l >= m])

Theta(theta) = ((1/2)*cos(2*theta)-1/2)^((1/2)*m)*(sin(2*theta)*hypergeom([(1/2)*m+(1/2)*l+1, (1/2)*m-(1/2)*l+1/2], [3/2], (1/2)*cos(2*theta)+1/2)*_C1+2^(1/2)*(1-cos(2*theta))^(1/2)*hypergeom([(1/2)*m-(1/2)*l, (1/2)*m+(1/2)*l+1/2], [1/2], (1/2)*cos(2*theta)+1/2)*_C2)/(1-cos(2*theta))^(1/2)

(3)

convert(Theta(theta) = _C1*((1/2)*cos(2*theta)-1/2)^((1/2)*m)*sin(2*theta)*hypergeom([(1/2)*m+(1/2)*l+1, (1/2)*m-(1/2)*l+1/2], [3/2], (1/2)*cos(2*theta)+1/2)/(1-cos(2*theta))^(1/2)+_C2*hypergeom([(1/2)*m-(1/2)*l, (1/2)*m+(1/2)*l+1/2], [1/2], (1/2)*cos(2*theta)+1/2)*(-2*cos(2*theta)+2)^(1/2)*((1/2)*cos(2*theta)-1/2)^((1/2)*m)/(1-cos(2*theta))^(1/2), `2F1`)

Theta(theta) = (1/2)*_C1*((1/2)*cos(2*theta)-1/2)^((1/2)*m)*sin(2*theta)*Pi^(1/2)*GAMMA(-(1/2)*m-(1/2)*l)*JacobiP(-(1/2)*m-(1/2)*l-1, 1/2, m, -cos(2*theta))/((1-cos(2*theta))^(1/2)*GAMMA(1/2-(1/2)*m-(1/2)*l))+_C2*Pi^(1/2)*GAMMA(1-(1/2)*m+(1/2)*l)*JacobiP(-(1/2)*m+(1/2)*l, -1/2, m, -cos(2*theta))*(-2*cos(2*theta)+2)^(1/2)*((1/2)*cos(2*theta)-1/2)^((1/2)*m)/((1-cos(2*theta))^(1/2)*GAMMA(-(1/2)*m+(1/2)*l+1/2))

(4)

``

 

Download question_12.19.mw

 

Hi

I  have a system of second order differential equation to be solved numerically. I would like to set up events to halt integration  to find the values of phi when r(phi)=2/3 . Here is my code

DE:=diff(1/r(phi),phi,phi)+(1/r(phi))=(G*M/h^2)+(3*G*M/c^2*r(phi)^2));

ics:=r(0)=2/3,D(r)(0)=0;G:=1;M:=1;h:=1;c:=1;

p:=dsolve({DE,ics},numeric,events=[[r(phi),r(phi),halt]],[diff(r(phi),phi)=0,halt]]);

The code only works for the second event so it halts for r(phi)=1.63... etc

How do i stop this?

 

Thanks for any help.

 

Differential equation solve

The differential equation I'm solving for is:

Differential Equation

Hi everyone,

I am a new user of maple and i want to know the procedures to follow when solving 4 differential equations simultaneously.

e.g

ds/dt=Λ0-βcSI/N-μS

dL/dt=Λ1+βcSI/N-μ1L+ΑcIT/N

dI/dt=kL-μ2I

dT/dt=r1L+r2I-ΑcIT/N-μT

Any help will be highly appreciated. Regards

Hello all, 

During my last attempt to solve ODE system (autonomous system which includes 3 first order diff. equations) with initial conditions, Maple had performed the solution which includes d_z1 parameter as follows below (I present the solution of one of the equations):

S(t)=S(0)∫(QN_z1+A)d_z1, where integral ∫ is defined integral from 0 to t, S(0) is the initial value of S, Q, N and A are the parameters. I would like to ask, what does it mean _z1 and d_z1? Why if the ODE system is only time dependent, I received the integral with other differential, that is d_z1? Does it mean that the integral can't be evaluated or maybe something else?

Thanks in advance,

Dmitry

 

 

Hey all new to Maplesoft my question is this;

2. Give the Maple command(s) to compute \frac{\partial^8 f}{\partial^5 x \partial^3 y} for f(x, y) = e^{2x+ cos(y)}.

The goal is to get Kalman Form

https://docs.google.com/file/d/0Bxs_ao6uuBDUT25BeVhtWjZwRUU/edit?usp=sharing

https://docs.google.com/file/d/0Bxs_ao6uuBDUVXU5dXh6Rl9zUUU/edit?usp=sharing

 

I am doing the example in page 707 of Partial Differential control theory Volume 2 by J.F.

 

when using Robertz Daniel's Ore and Involutive packages

 

with(Involutive):

with(OreModules):

Alg := DefineOreAlgebra(diff=[D,t...

Diff(x1(t),t) - x2(t) = 0;

Diff(x2(t),t) - x3(t) = 0;

Diff(x3(t),t) +3*x3(t) + 4*x2(t) + x1(t) = 2*Diff(u(t),t$2) + 5*Diff(u(t),t) + 7*u(t);

 

multiply above system by test functions -lambda1(t),-lambda2(t),-lambda3(t) and integrate by part

in order to find adjoint operator in the form

 

x1 -> Diff(lambda1(t),t) - lambda3(t) = miu1(t)

x2 -> Diff(lambda2(t),t) + lambda1(t) - 4*lambda3(t) = miu2(t)

Can maple use a Differential Operator somehow in the following sense?

Instead of expanding (D-p)^n where p is a constant and D the differential operator and n an integer and then in each term writing D^n(f) for some function can I just leave the expression as it is like

(D-p)^n and acting on everything on the right?

Hi every body

I want to solve a differential equation y'(t) = sqrt((f-1)/(t^f-t)) and get an answer in terms of ordinary function.is it possible. thanks 

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