# Items tagged with odeode Tagged Items Feed

### Error, (in dsolve/numeric/bvp) initial Newton iter...

January 12 2015
1 2

Dear All,

I am solving 6 ODE equations with boundary conditions using Runge kutta Felbergh 45 (Maple 12). then, i got this problem.. any suggestion??

Thank you :)

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 Error, (in dsolve/numeric/bvp) initial Newton iteration is not converging
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 Warning, unable to evaluate the function to numeric values in the region; see the plotting command's help page to ensure the calling sequence is correct
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### Comparison of analytic and numeric solution of 1. ...

January 08 2015
0 3

The link to the .mw file is underneath the content.

I was trying to solve the first order ode for x(t). pp1 and pp2 are essentially diff(x(t),t).

I just wanted to see them plottet. While deriving these equations (which stem from a first order nonlinear quadratic diff. eq.) I had to distinguish between those 2 solutions. Also I made the assumption that diff(x(t),t) everywhere so the only solution being allowed should be pp1. Oddly the analytic solution for pp2 looks like the numeric solution for pp1 and my question is: Why is that?

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### Analyzing a differential equation system with vary...

January 02 2015
0 5

Hi there,
I have a set of differential equations whose solution, Jacobian matrix and its eigenvalues, direction field, phase portrait and nullclines, need to be computed.

Each of the equations has a varying parameter.

I know how to get the above for a single parameter value, but when I set a range of values for the parameters, Maple is not able to handle all cases as I would expect: solving the differential equation system:

eq1 := x*(1.6*(1-(1/100)*x)-phi*y)
eq2 := (x/(15+x)-0.3e-1*x-.4)*y+.6+theta
desys := [eq1, eq2];
vars := [x, y];

Error, (in unknown) invalid input: Utilities:-SetEquations expects its 2nd argument, equations, to be of type set({boolean, algebraic, relation}), but received {-600*y+(Array(1..2, {(1) = 8400, (2) = 15900})), Array(1..5, {(1) = 0, (2) = 0, (3) = 0, (4) = 0, (5) = 0})}

The equations are the following:
de1 := diff(x(t), t) = x(t)*(1.6*(1-(1/100)*x(t))-phi*y(t));
de2 := diff(y(t), t) = (x(t)/(15+x(t))-0.3e-1*x(t)-.4)*y(t)+.6+theta

the parameters being:
phi:=[0 0.5 1 1.5 2]
theta:=[5. 10.]

How can I handle the situation so that Maple computes each of the above for each combination of the parameters?

I would like to avoid using two for loops and having to store all results in increasingly bigger and complicated arrays.

The worksheet at issue is this: MaplePrimes_Tumour_model_phi_theta_variation.mw

Thanks,
jon

### solving linear ODE systems--I wanted to use functi...

December 30 2014
1 4

I have solved ODE's with either i.c. or b.c. (mechanics stuff) where the results were in terms of expressions, not functions.  I could plot these expressions, substitute values in for parameters, etc.

Then I thought that the real way to solve an ODE or system of ODE's was to define functions.  I wanted this to be in three levels: the solutions in generality, the solutions with i.c./m.c. applied, and then further with the parameter values defined.

So far, no joy.  Lots of confusion--input eqns as sequence, list, set?  I looked on the Maple help page, thought I was doing things right. I even tried out "union" for the ode's and the ic's.

The code is below; statement (11) produces an error. Yes, I am using Maple 18, even though the file says Maple 15.  I'd like to solve the 4-ODE system at the three levels listed above, and then (if possible), plot the result! Am I asking too much?  Should I be using MapleSim or some other product instead?

Thanks for any and all help!

robert w.

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data:=(m1=1,m2=2,m3=1,c1=0,c2=0,c3=0,k1=5,k2=2,k3=2);

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### Set initial conditions for a dfieldplot...

December 29 2014
0 2

Hi there,

I have an ODE system which apparently needs some initial conditions to have its vector field plotted.

I am giving Maple's dfieldplot function the following arguments:

dfieldplot([de1, de2], [A(t), G(t)], t = 0..1, [A(0) = 25, G(0) = 0], A = 0..900, G = 0..200)

But Maple yields an error that reads:

Error, (in DEtools%2Fdfieldplot) invalid use of initial points or option - see phaseportrait

I would say that the initial conditions are correctly stated, according to the documentation of the function.

This is the attempt: MaplePrimes_Malaria_infection_cont.mw

Any ideas on what's missing?

Thanks,

jon

### Loop over a set of lists...

December 29 2014
0 2

Hi there,

I would like to have the Jacobian matrix of an ODE system evaluated, and their eigenvalues computed, at the steady states of the system.

I know how to get the Jacobian matrix evaluated and the eigenvalues computed on an individual basis, setting manually each steady state as the argument of the matrix.

However, I would like to have it in a loop, so that the loop manages all steady states, that is:

steadyStates:= solve(mySystem); # would yield a set of pairs/lists

m:=Jacobian(steadyStateN); # evaluate the Jacobian matrix

ev:= eigenvals(m); # compute the eigenvalues and save them to another variable/array and print them

end for:

First, I am not to find a way to loop over my steadyStates.

Attached is an example where the Jacobian matrix and eigenvalues are computed individually, where the steady states have been hard-coded once they have been computed: MaplePrimes_Predator_prey_model_Jacobian.mw

Any ideas on how to do this?

Thanks,

jon

### Compute and display isoclines (nullclines) for an ...

December 29 2014
0 2

Hi there,

I would like to compute and display the nullclines of a set of ordinary differential equations.

AFAIK, I can compute the nullclines in Maple by defining the equations and solving the system

e.g.:

# Define the equations
eq1 := u(t)*(1-u(t)/kappa)-u(t)*v(t) = 0;
eq2 := g*(u(t)-1)*v(t) = 0;

# Solve the system (i.e. compute the nullclines)
sol := solve({eq1, eq2}, {u(t), v(t)});

However, I am not quite able to imagine how to display them over a dfieldplot or a phaseportrait.

Attached is an example with some differential equations, and their vector field and trajectories: MaplePrimes_Predator_prey_model_nullclines.mw.

It can be use to illustrate how to (compute and) display the nullclines.

Thank you,

jon

### How to check that dsolve was successful?...

December 25 2014
2 2

I am also not sure how to program a check in the code to determine that dsolve solved the differential equation.

For example

ode:=diff(y(x),x)-a*(x^n-x)*y(x)^3-y(x)^2=0;
sol:=dsolve(ode,y(x));

In this case, sol is () as it could not solve it. When I tried odetest, I get an error

odetest(sol,ode);

Error, invalid input: odetest uses a 2nd argument, ODE, which is missing

What is the correct way to check dsolve was successful that will work for all cases? I am looking for programmable method, no GUI use.

### How to plot numerical solution of ODE system?...

December 22 2014
0 2

Hallo. I'm solving a initial value problem for system of 7 ODE:

dsn := dsolve({expand(maineq[1, 1]), expand(maineq[1, 2]), expand(maineq[1, 3]), expand(maineq[1, 4]), expand(maineq[1, 5]), expand(maineq[1, 6]), expand(maineq[1, 7]), T(0) = .5, u(0) = u0, Y[1](0) = .8, Y[2](0) = .2, Y[3](0) = 0, Y[4](0) = 0, Y[5](0) = 0}, numeric, method = lsode[backfull])

Is there easy way how to plot result?

### Solving non-linear ODE...

December 17 2014
2 22

Hi,

I'm trying to solve the following non-linear ODE numerically:

by ececuting

but maple gives me this error-message:

"Error, (in dsolve/numeric/make_proc) Could not convert to an explicit first order system due to 'RootOf'"

I couldnt find any useful information in the manual. What does this error mean? Is there something wrong with my maple code or is there just no solution for this particulare differential equation?

### Second order ODE with infinity condition...

December 15 2014
1 1

I got a problem with solving a second order ODE.

The ODE is :

-V(xi)+(1/2)*xi*(diff(V(xi), xi))+(1/4)*(diff(V(xi), xi, xi))=-(1/2)*k2*(diff(H(xi), xi))-k1*n*X/E+1+k2

where k1,k2,n,X,E  all are constant.

the condition is :

V(xi) tends to 2*xi^2 as xi tends to infinity.

I used 'dsolve' to solve the equation firstly, and got a solution with two constant C1 and C2, I want to use the condition to elimilate C2, so I used limit(sol,xi=infinity)=2*xi^2. But when I used the command 'limit', I can't get the answer.

Could any one help me?

Many thanks!!!

### How to solve non-linear ODE numerically...

December 13 2014
2 3

Hi,

I'm trying to solve the following differential equation numerically with dsolve:

but dsolve gives me this error:

> res := dsolve(DGL, numeric, parameters = [y0, A, B, C, E]);
Error, (in DEtools/convertsys) unable to convert to an explicit first-order system

I think the problem is that I use the wrong solver. Does Maple provide a solver which is capable of solving this kind of equations (nonlinear ODE)?

### Error, (in isolate) cannot isolate for a function ...

December 10 2014
0 17

Hello,

Im solving 4 ODE equations with BC. im trying to shoot the initial value but im having this error:

""Error, (in isolate) cannot isolate for a function when it appears with different arguments""

anyone could help me???

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 Error, (in isolate) cannot isolate for a function when it appears with different arguments
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December 09 2014
0 3

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### How to plot the Taylor Polynomial approximation...

December 08 2014
0 2

Hi everyone, I have been trying to plot the Taylor Polynomial approximation with the following code. However, my maple crushes everytime I run it. I indexed some of the variables to get the plot. The code works fine without the index. What did I do wrong?

y := array(1 .. 2);

Digits := 10;

n := 30;

h := .1;

T := 0;

X := 1;

f := (x, t) -> 1/(3*x(t)-t-2);

one := 1/(3*x(t)-t-2);

two := diff(f(x, t), t);

first := diff(x(t), t)

for k to n do

y[1] := subs(t = T(k), x(T(k)) = X(k), one);

y[2] := subs(first = y[1], t = T, x(T(k)) = X(k), two);

X[k+1] := X+sum(y[i]*h^i/factorial(i), i = 1 .. 2);

T[k+1] := T+h

end do;

X[n];

data := [seq([T[n], X[n]], n = 0 .. 30)];

p[2] := plot(data, style = point, color = blue);

p[3] := plot(data, style = line, color = blue);
display(p[2],  p[3])

The code without Index (which works fine)

y := array(1 .. 2);

Digits := 10;

n := 30;

h := .1;

T := 1;

X := .1547196278;

f := (x, t) -> 1/(3*x(t)-t-2);

one := x(t)^4*e^t-(1/3)*x(t);

two := diff(f(x, t), t);

first := diff(x(t), t);

for k to n do

y[1] := subs(t = T, x(T) = X, one);

y[2] := subs(first = y[1], t = T, x(T) = X, two);

X := X+sum(y[i]*h^i/factorial(i), i = 1 .. 2);

T := T+h

end do

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