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i am solving 3 ODE with boundary condition.. with boundary condition

 

b.mw

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

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then i got this error

Error, (in dsolve/numeric/bvp) initial Newton iteration is not converging

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

 

Dear Friends,

My present problem is to calculate the coefficients  

of ODES based on the experiment data. In order to simulate the actual experiment, a set of  is given with . Then the experiment data (yexp) can be calculated. Finally, the least-squares method (lsq) is used to calculate the coefficient values. Now the NLPSolve function can be used. However, the globalsolve cant run.

 

If it is convenient for you, wish you can solve it.

 

Code:

 

restart;
cdm_ode := diff(y1(t), t) = c0*(y6(t)*(1-y3(t))/(s0*(1-y4(t)*(1-y5(t)))))^n/(1-y2(t)), diff(y2(t), t) = ks*y2(t)^(1/3)*(1-y2(t)), diff(y3(t), t) = h1*(1-y3(t)/h2)*c0*(y6(t)*(1-y3(t))/(s0*(1-y4(t)*(1-y5(t)))))^n/(sigma*(1-y2(t))), diff(y4(t), t) = (1/3)*kp*(1-y4(t))^4, diff(y5(t), t) = A*B*y1(t)^(B-1)*c0*(y6(t)*(1-y3(t))/(s0*(1-y4(t)*(1-y5(t)))))^n/(1-y2(t)), diff(y6(t), t) = y6(t)*c0*(y6(t)*(1-y3(t))/(s0*(1-y4(t)*(1-y5(t)))))^n/(1-y2(t));

 

tol_t := 3600;
sol := dsolve([cdm_ode, y1(0) = 0, y2(0) = 0, y3(0) = 0, y4(0) = 0, y5(0) = 0, y6(0) = 175], numeric, range = 0 .. tol_t, output = listprocedure, parameters = [c0, n, sigma, s0, ks, h1, h2, kp, A, B]);

sol(parameters = [5.7*10^(-6), 10.186, 175, 200, 5*10^(-8), 10000, .269, 1.5*10^(-7), 1.5, 2]);

t := [seq(i^2, i = 0 .. 50, 1)];

y1data := subs(sol, y1(t));
 
y1exp := [seq(y1data(t[i]), i = 1 .. 51)];

err := proc (c0, n, s0, ks, h1, h2, kp, A, B) local y1cal, y1val, lsq; sol(parameters = [c0, n, 175, s0, ks, h1, h2, kp, A, B]); y1cal := subs(sol, y1(t)); y1val := [seq(y1cal(t[i]), i = 1 .. 51)]; lsq := add((y1val[i]-y1exp[i])^2, i = 1 .. 51); lsq end proc;

with(Optimization);
val := NLPSolve(err, 10^(-8) .. 10^(-4), 2 .. 20, 150 .. 250, 10^(-2) .. 1, 100 .. 20000, 10^(-5) .. .4, 10^(-5) .. 1, .5 .. 2, 1 .. 10);
GlobalSolve(err, 10^(-10) .. 10^(-4), 2 .. 20, 150 .. 250, 0 .. 1, 100 .. 15000, 0 .. .5, 0 .. 1, .5 .. 2, 1 .. 5);


Error, (in GlobalOptimization:-GlobalSolve) `InertForms` does not evaluate to a module

 

 

 

 

 

i am solving 3 ODE question with boundary condition. when i running the programm i got this error.. any one could help me please.. :)

NULL

restart; with(plots); k := .1; E := 1.0; Pr := 7.0; Ec := 1.0; p := 2.0; blt := 11.5

Eq1 := diff(f(eta), eta, eta, eta)+f(eta)*(diff(f(eta), eta, eta))+Gr*theta(eta)-k*(diff(f(eta), eta))+2*E*g(eta) = 0;

diff(diff(diff(f(eta), eta), eta), eta)+f(eta)*(diff(diff(f(eta), eta), eta))+Gr*theta(eta)-.1*(diff(f(eta), eta))+2.0*g(eta) = 0

(1)

Eq2 := diff(g(eta), eta, eta)+f(eta)*(diff(g(eta), eta))-k*g(eta)-2*E*(diff(f(eta), eta)) = 0;

diff(diff(g(eta), eta), eta)+f(eta)*(diff(g(eta), eta))-.1*g(eta)-2.0*(diff(f(eta), eta)) = 0

(2)

Eq3 := diff(theta(eta), eta, eta)+Pr*(diff(theta(eta), eta))*f(eta)+Pr*Ec*((diff(f(eta), eta, eta))^2+(diff(g(eta), eta))^2) = 0;

diff(diff(theta(eta), eta), eta)+7.0*(diff(theta(eta), eta))*f(eta)+7.00*(diff(diff(f(eta), eta), eta))^2+7.00*(diff(g(eta), eta))^2 = 0

(3)

bcs1 := f(0) = p, (D(f))(0) = 1, g(0) = 0, theta(0) = 1, theta(blt) = 0, (D(f))(blt) = 0, g(blt) = 0;

f(0) = 2.0, (D(f))(0) = 1, g(0) = 0, theta(0) = 1, theta(11.5) = 0, (D(f))(11.5) = 0, g(11.5) = 0

(4)

L := [10, 11, 12];

[10, 11, 12]

(5)

for k to 3 do R := dsolve(eval({Eq1, Eq2, Eq3, bcs1}, Gr = L[k]), [f(eta), g(eta), theta(eta)], numeric, output = listprocedure); Y || k := rhs(R[3]) end do

Error, (in dsolve/numeric/bvp) initial Newton iteration is not converging

 

R

R

(6)

plot([Y || (1 .. 3)], 0 .. 10, labels = [eta, (D(f))(eta)]);

Warning, unable to evaluate the functions to numeric values in the region; see the plotting command's help page to ensure the calling sequence is correct

 

 

NULL

NULL


Download tyera(a).mw

calculs using Maple...

November 01 2014 sarra 215

Dear all;

Thank you very much is you can make the computation using maple.

I have this system:

x'(t)=x*y-x^2*y+y^3;

y'(t)=y^2+x^3-x*y^2;

I would like to make to change the system in another system using polar coordinate: like x=r*cos(theta) and y=r*sin(theta), and then derive a simple system: r'=F(r, theta) and theta'=G(r, theta), where here F and G are two unknowns functions. 

Many thinks if someone can help me using a Maple code. 

 

Hi every body:

i have a second order ode and will convert to two ode of first order with maple,how do this work???

eq := diff(y(x), x, x)+2*y(x)+y(x)^2 = 0

Let N be an integer. 

 

For each pair of integers (n,m) where 1<= n,m <= N, we have a variable f_{n,m}(t). 

 

Then for these we have a system of ODEs 

 

d/dt f_{n,m}(t) = \sum_{n', m'} f_m'n' * f_m''n'' * (m'n'' - m''n') 

 

where m''=m-m', n''=n=n', and the sum is simply over for all pairs (n',m'). 

 

I simply do not know how to put these set of equations into Maple in a nice way. 

 

I will really appreciate any help!

I'm trying to solve this system of ODEs by Laplace transform. 

> de1 := d^2*y(t)/dt^2 = y(t)+3*x(t)

> de2 := d^2*x(t)/dt^2 = 4*y(t)-4*exp(t)

with initial conditions 

> ICs := y(0) = 2, (D(y))(0) = 3, x(0) = 1, (D(x))(0) = 2

 

Using 

> deqns := de1, de2

and

> var := y(t), x(t)

 

I need to solve it for both y(t) and x(t), I have tried this by:

> dsolve({ICs, deqns}, var, method = laplace)

And

> dsolve({ICs, deqns}, y(t), method = laplace)

> dsolve({ICs, deqns}, x(t), method = laplace)

 

However I get this error message:

Error, (in dsolve/process_input) invalid initial condition

 

Any help is appreciated

Hello,

 

could you help me solve this error ? I don't understand what it means.

 


> eq3:=diff(x(t),t,t)+Gamma*diff(x(t),t)+omega[0]^2*(x(t)-(diff(x(t),t,t)+Gamma*diff(x(t),t)+omega[0]^2*x(t)+omega[0]^2*X[0])/omega[0]^2) = -omega[0]^2*X[0]:
> dsolve(eq3);
Warning, it is required that the numerator of the given ODE depends on the highest derivative. Returning NULL.

 

Thanks.

bifurcation diagram...

September 29 2014 sarra 215

Hi,

I have a non linear ode with sinosoial term, (sin(x)).

How can we Analyse the system and plot the bifurcation diagram:

x'=r*x-sin(x);

Thank you very much for your help.

 

Hi

I have three system of ODE and i would like to solve it using Homotopy perturbation method. Could you please provide to me the code in Maple or the Maple pachage that used to solve it by Homotopy perturbation method ?

I hope to hear you soon

Sara

 

Hi.

I need you to answer to thos question using maple,

I have x'(t)=e^{2*x(t)}  + alpha -2*x(t),  where alpha is a constant in R.

I would like to compute the equilibrium points and if there is a saddle-node bifurcation.

Thank you very much.

 

Good day, can any one help in writing maple programme for the finite difference (FD) formulae define to solve this coupled non-linear  ODEs. See it here FDM_programme.mw Thank you

NOTE: please disregard the earlier link.

Hi I am simply trying to rearange equation X, the steoes I want to do are differentiate X w.r.t t then insert equation Y into the new differentiated form but I am stuck, I am not really sure what to try I have used algsubs but it comes up with an error.

 

here is my code: 

 

X := diff(x(t), t)+(k1+k2+k3)*x(t)-(k4-k1)*y(t)-k1 = 0;
print(`output redirected...`); # input placeholder
/ d \
|--- x(t)| + (k1 + k2 + k3) x(t) - (k4 - k1) y(t) - k1 = 0
\ dt /
Y := diff(y(t), t)+(k4+k5+k6)*y(t)-(k3-k6)*x(t)-k6 = 0;
print(`output redirected...`); # input placeholder
/ d \
|--- y(t)| + (k4 + k5 + k6) y(t) - (k3 - k6) x(t) - k6 = 0
\ dt /
A := diff(X, t);
print(`output redirected...`); # input placeholder
/ d / d \\ / d \
|--- |--- x(t)|| + (k1 + k2 + k3) |--- x(t)|
\ dt \ dt // \ dt /

/ d \
- (k4 - k1) |--- y(t)| = 0
\ dt /
algsubs(Y, A);
%;
Error, (in algsubs) cannot compute degree of pattern in y(t)

 

Hi all

I have written the following code in maple to approximate arbitrary functions by hybrid of block-pulse and bernstein functions but it doesn't work properly especially for f(t)=1.0, so what is the matter?

bb1.mws

 


best wishes

Mahmood   Dadkhah

Ph.D Candidate

Applied Mathematics Department

Hi

I'm dealing with 2nd order ODE on Maple. By using " infolevel 5" Maple tell me that it use Kovacic's algorithm to find the solution. Could anybody tell me how or at least some idea so that I can go on this my self. Following here my ODE

Thank you so much

Chaimongkol

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