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Solve This Equation...

February 14 2014 Ratch 211

Can anyone tell me how to solve the equation above using Maple.  I know that there is a solution around x=0.995, y=0.743, but I cannot induce Maple to find it.  Any help or suggestions would be appreciated.

Ratch

 

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!

Hello, 

So I have two simultaneous equations, 

T= n1/(1+|T-S|) and S=n2/(n3+|T-S|) 

Where n1, n2 and n3 are constant parameters (from here on I fix n1=1 and n3=0.3). So I want to plot T, S against n2 for different values of n2. 

If I also fix n2 (say, n2=1.5) I  can get values for T and S no problem. 

But I've no idea (after many hours of searching) how to progresss. I know I need the program to put various values of n2 into the two equations and then plot the solutions numerically but I'm unsure what to try next.

Could anyone please shed some light on this?!

Thanks!

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

I am trying to get a solution to the heat equation with multiple boundary conditions.

Most of them work but I am having trouble with two things: a Robin boundary condition and initial conditions.

First, here are my equations that work:

returns a solution (actually two including u(x,y,z,t)=0).

 

However, when I try to add:

or

 

I no longer get a solution.

 

Any guidance would be appreciated.

 

Regards.

 

I have uploaded a worksheet with the equations...

Download heat_equation_pde.mw

Can we define/set a range in Maple. e.g 


I have the following equation:

y = 1.048 + 1.02*x + 6.118*(z-4.041*x^2) + 16.22*(z^2) +6.241* (x*z)

The value of z is within 0.001 - 0.543, y is from 1 - 12 and x is from 0.001 - 0.7

How should I define it in Maple, so while solving equations it read the values within the given range? 


i have got alot of mixed and high degree derivatives. For example:

u[x]*u[x,t]*eta[x,t]+u[]^2*u[x]*eta[x]+kis(x,y)u[x,t]^2*u[]+eta(x, y)*u[]*u[x]^2+ksi[x,t]*u[x]^2*u[x,t]+......

like this alot of terms

my question is how can i solve divided by the derivative of the u(x,t) partial differential equations system and so  how can i find eta(x,t,u) and ksi(x,t,u) 

Hi everybody,

Suppose that in an equation, I have the term x/(t).  I want to substitute it by v(t).  Any suggestion because I am trying but don't find an help page on this.

 

Thank you in advance for your help!

 

--------------------------------------
Mario Lemelin
Maple 17.01 Ubuntu 13.10 - 64 bits
Maple 17 Win 7 - 64 bits messagerie : mario.lemelin@cgocable.ca téléphone :  (819) 376-0987

I am trying to solve a set of equations for a Fluid dynamics problem and I cannot get a result...Any ideas why?

rho := 1.184;
nu := 1.562*10^(-5);
ID := .15;
L := 24.5;
Kl := 12.69;
Ho := 50.52;
a := 2.1*10^(-5);
E := 0.1e-2; alpha := 1.05;

sys := {Re = ID*V/nu, hl = (f*L/ID+Kl)*V^2/(2*9.81), Vflow = (1/4)*Pi*ID^2*V, Hrequired = alpha*V^2/(2*9.81)+hl, Hrequired = -a*Vflow^2+Ho, 1/sqrt(f) = -1.8*log[10](6.9/Re+(E/(3.7))^1.11)};

solve(sys*{Re, V, f, hl, Vflow, Hrequired});
%;
Error, (in unknown) invalid input: Utilities:-SetEquations expects its 2nd argument, equations, to be of type set({boolean, algebraic, relation}), but received {{Re = (9603072983/1000000)*V, hl = (5096839959/100000000000)*((1633333333/10000000)*f+1269/100)*V^2, Vflow = (9/1600)*Pi*V, Hrequired = (5351681957/100000000000)*V^2+hl, Hrequired = -(21/1000000)*Vflow^2+1263/25, 1/f^(1/2) = -(9/5)*ln((69/10)/Re+27367561/250000000000)/ln(10)}}

 

Hello

I calculated following two expressions, x1,and x2.

x1:=map(f,a+b);

x2:=map(f,y=a+b);

 

The results of these are

f(a) + f(b)

f(y) = f(a + b)

for each. And, I can understand the logic of this.

 

If I want to derive the result of x2 as f(y)=f(a)+f(b), how should I do about x2?

Isn't there other way than to write

map(f, lhs(x2))=map(f,rhs(x2))

?

Please teach me this.

Thank you in advance.

Taro

 

 

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?

 

Hello, how can i solve these equations

eq[1]:=a'[1](t)*p[1](x)+b*a[1](t)*p[1](x)

eq[2]:=a'[2](t)*p[2](x)+b*a[2](t)*p[2](x)

eq[3]:=a'[3](t)*p[3](x)+b*a[3](t)*p[3](x)

eq[4]:=c[1]*a[1](t)+c[2]a[2](t)+c[3]a[3](t)-q(t)

eq[5]:=d[1]*a[1](t)+d[2]a[2](t)+d[3]a[3](t)-p(t),

where p[i](x) , c[i] , d[i] , q(t) and p(t) are known functions?

I have to questions. One is the main one, about simplifying fractions.

This is equations.

jj:=L*theta*gamma[2]^2*(-1+alpha)/(delta[2]*(-alpha*gamma[1]^(-2*sigma+2)*gamma[2]^(2*sigma)-gamma[2]^2+gamma[2]^2*alpha));

kk:=expand(denom(jj)/gamma[2]^2);

ll:=op(1,kk);

mm:=simplify(ll,power);

nn:=mm-delta[2]+delta[2]*alpha;

oo:=numer(jj)/gamma[2]^2/nn;

pp:=(numer(jj)/gamma[2]^2)/(denom(jj)/gamma[2]^2);

 

From now, I will explain. Though as I don't know how to put a maple screen on this board I think I will have you feel some inconvenience, please forgive it.

I want to make jj more simple, dividing both of numerator and denominator of jj, with gamma[2]^2.

But, what I could at best was this. First, taking denominator of jj and deviding it with gamma[2]^2 and expanding it like kk. Second, as the first term among that expression had terms of gamma[2] on both of the numer and denom, I picked out the first term as ll in the above maple commands, and simplified it with option: power, in mm. Thirdly, I rewrote kk as in nn.

and Forthly, I rewrote jj with modification of deviding numerator and denominator with gamma[2]^2, using the result which I could get as I wrote above. oo is that. And the result of oo is what I wanted to get.

But, on the other hand, when i divided denom and numer of jj directly by gamma[2]^2, the result I can get then is not 

good one: the output of pp is not what I wanted to get.

Is there more simple way to do what I did in the above? This is a first question.

 

And, another is how I can post the screen of maple on this question board?

 

I hope you will answer my question. I thank all of you who will answer these question in advance.

 

 

 

 

Dear people being here,

I have a question.

When I wrote as

aa:=(delta[1]*n[1])/(n[f1]*delta[1]);

maple returned as 

aa := n[1]/n[f1]

How can I have maple express the original one, aa:=(delta[1]*n[1])/(n[f1]*delta[1]), not what returned to me?

I hope you will answer to my question.

And, thanks in advance.

 

taro

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