Maple 17 Questions and Posts

These are Posts and Questions associated with the product, Maple 17

Hi there,

I am trying to maximize a function given a set of values to a parameter in the function. The function is an differential equation belonging to a system of two differential equations.

I have a for loop to state different values to the parameter.

Maple yields the error:

Error, (in Optimization:-NLPSolve) cannot evaluate the solution further right of 0.17757507e-4, probably a singularity

When trying to maximize the function.

Supposed that I was doing something wrong in the loop, if I reproduce the contents of the loop outside, and set a value for the parameter. If I plot the solution of the ordinary differential equation, I can see where the maximum lies.

Having plot it, the Optimizamtion:-Maximize works as expected.

However, omitting the plot has a weird effect: I only get the same result depending on the bounds I set for the Maximization:

de1 := diff(A(t), t) = r*m*(1-g)*A(t)-piecewise(t < 8, r*A(t), t >= 8, (r+k)*A(t));
de2 := diff(G(t), t) = r*m*g*A(t)-l*G(t);

ics := A(0) = 25.0, G(0) = 0.;
num := dsolve({de1, de2, ics}, {A(t), G(t)}, type = numeric, output = listprocedure, parameters = [g]);

num(parameters = [g = .15]);
val := eval(G(t), num);

# odeplot(val, [t, G(t)], t = 0 .. 100);


Maximize(val);
Error, (in Optimization:-NLPSolve) cannot evaluate the solution further right of 0.17757507e-4, probably a singularity

val2 := Maximize(val);

Error, (in Optimization:-NLPSolve) cannot evaluate the solution further right of 0.17757507e-4, probably a singularity

val3 := Maximize(val(t), t = 0 .. 60);

  [10267.824035766165, [t = 8.25727747134303]]

val4 := Maximize(val(t), t = 0 .. 100);

[6.863211343195069e-9, [t = 59.84184367042171]]

 

The right answer is [10267.824035766165, [t = 8.25727747134303]]: Why do I get two different answers even if in that range there is only one relative maximum?

I ignore whether the way I am specifying the arguments for the Maximize function is correct. val is a procedure.

 

What am I missing?

Attached is the worksheet: MaplePrimes_malaria_param_variation_2.mw

 

Thanks,

jon

Good day everyone, could you please help use Gauss Elimination method for these system of equations. See the worksheet here F1.mw

Thanks.

Hi there,

this may be a common task but did not find any helpful hint nor an answer: is there any way to combine to arrays A and B into another one element-wise, i.e.:
C = [[A[1],B[1]], [A[2],B[2]],...,[A[N],B[N]]]
without doing a for loop?


Thanks,
jon

Hi there,

I would like to have an operator (in this case, the natural logarithm) applied to a list/array of points defined as:

ydata := [0.572594976618e-1, 0.327865007249e-1, 0.280821589546e-1, 0.114365745192e-1, 0.578537931608e-2, 0.139154661062e-2, 0.641467839994e-3, 0.18013801847e-3];

How can I apply Maple's ln() operator to the whole array (i.e. avoid to apply it to ydata [1], ydata [2], etc.)?

Thank you,

jon

 

Hello friends!

I 'm a student and I don't know a lot about Maple, so I would be really grateful if anyone could help me.

I want to solve a system of two equations and I have two unknowns, which are k and εα. However I don't know what I am doing wrong and I can't solve it.

I have attached my file.

Thank you very much in advance!agogos_2.mw

 

How do I get values out of solved augmented matric in 2D math input? I cannot simply assign the solutions to a value by x:=A[1,5}, because it's an augmented matrix.

Can maple solve maximization problem like

q := proc (a, b, c) options operator, arrow; .2*b+.1*c end proc;
print(`output redirected...`); # input placeholder
(a, b, c) -> 0.2 b + 0.1 c
w := proc (a, b, c) options operator, arrow; .7*a+.1*c end proc;
print(`output redirected...`); # input placeholder
(a, b, c) -> 0.7 ab + 0.1 c
e := proc (a, b, c) options operator, arrow; .7*a+.2*b*c end proc;
print(`output redirected...`); # input placeholder
(a, b, c) -> 0.7 a + 0.2 b c

with(Optimization)

Maxmize(int(min(100+(.7*a+q)*(1/2), a), q)+int(min(100+(.2*b+w)*(1/2), b), w)+int(min(100+(.1*c+e)*(1/2), c), e)-a-b-c-ab-ac-bc)

Error, (in Optimization:-NLPSolve) cannot convert procedures to piecewise

 

 

Thanks alot if you can help me.Urgent! Really appreciate.

 

Dear Maple users,

My problem is as follows:

I have a factor base [2,3,5,7,11,33,34,35,36,37,38,39,40]

The numbers from 2 till 11 are primes, the rest is not. 

Then I have to factor (H+c1)(H+c2) in numbers of the factor base , where c1 and c2 go from 1 to some pre-defined limit. H=32 in my case.
And then I have to put the powers of the numbers of the factor base in a matrix. For example: (H+1)(H+1)=33² but also (H+1)(H+1)=3²*11².

That will become in matrix form [0 , 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0 ] but also (!) [0 , 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0 ].

This is not what I want! I want no double representations....

What I want is that (H+c1)(H+c2) should be represented in primes in the matrix if possible and else just represented as the other numbers.

 

hope you guys can help me!

Please I need someone to help out with how to solve the below ODE numerically using finite difference method with the necessary maple code:

 

█( S〗_h〗^' (t)=Λ_h-αβ_m I_v S_h-μ_h S_h+πI_m,  

〖I_m〗^' (t)=αβ_m I_v S_h-(σ_m+π+μ_h ) I_m

〖 S〗_v〗^' (t)=Λ_v-αβ_v I_m S_v-μ_v S_v

〖I_v〗^' (t)=αβ_v I_m S_v-μ_v I_v )

The initial conditions can be assumed. Suppose i want to include controls, how do I solve the problem and equally plot the graph.

 

Thank you.

ADENIYI MICHAEL

 

error in( dsolve/numeric/bvp) unable to achieve the requested accuracy of 0.1e-5 with maximum 128 point mesh (was able to get 0.22e-4), consider increasing `maxmesh` or using larger `abserr`

 

The above is the error message displayed by maple 17. How do I correct this.

Thank you.

 

Adeniyi Michael

I am numerically solving a nonlinear system of nine equations. How long can I expect it to take?

I have run it for 30 minutes and it has not solved yet.

Here is the system of equations:

0=Lambda-mu.*S-beta.*(H+C+C1+C2).*(S./N)-tau.*(T+C).*(S./N);

0=tau.*(T+C).*(S./N)-beta.*(H+C+C1+C2).*(T./N)-(mu+mu_T).*T;

0=beta.*(H+C+C1+C2).*(S./N)-tau.*(T+C).*(H./N)-(mu+mu_A).*H;

0=beta.*(H+C+C1+C2).*(T./N)+tau.*(T+C).*(H./N)-(mu+psi.*mu_A+mu_T+lambda_T).*C;

0=lambda_T.*C-(mu+mu_A+rho_1+eta_1).*C1;

0=rho_1.*C1-(mu+mu_A+rho_2+eta_2).*C2;

0=eta_1.*C1-(mu+rho_1+gamma).*CT1;

0=eta_2.*C2-(mu+rho_2+gamma.*(rho_1)./(rho_1+rho_2)).*CT2+(rho_1).*CT1;

0 = N - S - T - H - C - C1 - C2 - CT1 - CT2;

and I have numeric values for Lambda, beta, tau, mu, mu_T, mu_A, rho_1, rho_2, psi, gamma. The only parameters left are eta_1, eta_2.

Thank you.

I have used the command "op" in a code that I have written with Maple 17. When I restart the maple server and run the whole code again, the result of the "op" command changes! why is this happening?

As I am trying to solve this integration:

restart; with(linalg); with(stats); with(plots); with(Statistics); with(LinearAlgebra); with(Optimization);
lambda0 := proc (t) options operator, arrow; gamma0+gamma1*t+gamma2*t^2 end proc;
lambda := lambda0(t)*exp(beta*s);
t1 := 145; t3 := 250; t2 := (t1+t3)*(1/2);
s := 1/(273.16+50); s1 := 1/(273.16+t1); s3 := 1/(273.16+t3); s2 := 1/(273.16+t2); gamma0 := 0.1e-3; gamma1 := .5; gamma2 := 0; beta := -3800;
c := 300; n := 200;
Theta := solve(1-exp(-(gamma0*tau1+(1/2)*gamma1*tau1^2+(1/3)*gamma2*tau1^3)*exp(beta*s1)) = 1-exp(-(gamma0*a+(1/2)*gamma1*a^2+(1/3)*gamma2*a^3)*exp(beta*s2)), a);

a := Theta[1];

Delta := solve(1-exp(-(gamma0*(a+tau2-tau1)+(1/2)*gamma1*(a+tau2-tau1)^2+(1/3)*gamma2*(a+tau2-tau1)^3)*exp(beta*s2)) = 1-exp(-(gamma0*b+(1/2)*gamma1*b^2+(1/3)*gamma2*b^3)*exp(beta*s3)), b);

b := Delta[1];

A1 := `assuming`([unapply(int(exp(beta*s1)*exp(-(gamma0*t+(1/2)*gamma1*t^2+(1/3)*gamma2*t^3)*exp(beta*s1))/(gamma0+gamma1*t+gamma2*t^`2`), t = N .. M), N, M)], [N > 0, M > 0]);
A2 := unapply(int(exp(beta*s2)*exp(-(gamma0*(a+t-tau1)+(1/2)*gamma1*(a+t-tau1)^2+(1/3)*gamma2*(a+t-tau1)^3)*exp(beta*s2))/(gamma0+gamma1*(a+t-tau1)+gamma2*(a+t-tau1)^2), t = N .. M), N, M);
A3 := unapply(int(exp(beta*s3)*exp(-(gamma0*(b+t-tau2)+(1/2)*gamma1*(b+t-tau2)^2+(1/3)*gamma2*(b+t-tau2)^3)*exp(beta*s3))/(gamma0+gamma1*(b+t-tau2)+gamma2*(b+t-tau2)^2), t = N .. M), N, M);
B1 := `assuming`([unapply(int(t^2*exp(beta*s1)*exp(-(gamma0*t+(1/2)*gamma1*t^2+(1/3)*gamma2*t^3)*exp(beta*s1))/(gamma2*t^2+gamma1*t+gamma0), t = N .. M), N, M)], [N > 0, M > 0]);
B2 := unapply(int((a+t-tau1)^2*exp(beta*s2)*exp(-(gamma0*(a+t-tau1)+(1/2)*gamma1*(a+t-tau1)^2+(1/3)*gamma2*(a+t-tau1)^3)*exp(beta*s2))/(gamma0+gamma1*(a+t-tau1)+gamma2*(a+t-tau1)^2), t = N .. M), N, M);
B3 := unapply(int((b+t-tau2)^2*exp(beta*s3)*exp(-(gamma0*(b+t-tau2)+(1/2)*gamma1*(b+t-tau2)^2+(1/3)*gamma2*(b+t-tau2)^3)*exp(beta*s3))/(gamma0+gamma1*(b+t-tau2)+gamma2*(b+t-tau2)^2), t = N .. M), N, M);

F0 := A1(0, tau1)+A2(tau1, tau2)+A3(tau2, c);
F1 := B1(0, tau1)+B2(tau1, tau2)+B3(tau2, c);

NLPSolve(1/(n^3*(F0*F1-F1)), tau1 = 115 .. 201, tau2 = 237 .. 273);

I need to have tau1 tau2 as varibles to get there optimal values ..

But this error keeps coming :


Error, (in Optimization:-NLPSolve) integration range or variable must be specified in the second argument, got HFloat(1.0) = HFloat(158.0) .. HFloat(255.0)

Please Help ..

I am a problem with solve differential equation, please help me: THANKS 

g := (y^2-1)^2; I4 := int(g^4, y = -1 .. 1); I5 := 2*(int(g^3*(diff(g, y, y)), y = -1 .. 1)); I6 := int(g^3*(diff(g, y, y, y, y)), y = -1 .. 1); with(Student[Calculus1]); I10 := ApproximateInt(6/(1-f(x)*g)^2, y = -1 .. 1, method = simpson);

dsys3 := {I4*f(x)^2*(diff(f(x), x, x, x, x))+I5*f(x)^2*(diff(f(x), x, x))+I6*f(x)^3 = I10, f(-1) = 0, f(1) = 0, ((D@@1)(f))(-1) = 0, ((D@@1)(f))(1) = 0};

dsol5 := dsolve(dsys3, numeric, output = array([0.]));

              Error, (in dsolve/numeric/bvp) system is singular at left endpoint, use midpoint method instead

****************FORMAT TWO ********************************************************

g := (y^2-1)^2; I4 := int(g^4, y = -1 .. 1); I5 := 2*(int(g^3*(diff(g, y, y)), y = -1 .. 1)); I6 := int(g^3*(diff(g, y, y, y, y)), y = -1 .. 1); with(Student[Calculus1]); I10 := ApproximateInt(6/(1-f(x)*g)^2, y = -1 .. 1, method = simpson);
dsys3 := {I4*f(x)^2*(diff(f(x), x, x, x, x))+I5*f(x)^2*(diff(f(x), x, x))+I6*f(x)^3 = I10, f(-1) = 0, f(1) = 0, ((D@@1)(f))(-1) = 0, ((D@@1)(f))(1) = 0};

dsol5 := dsolve(dsys3, method = bvp[midrich], output = array([0.]));
%;
                                   Error, (in dsolve) too many levels of recursion

I DONT KNOW ABOUT THIS ERROR

PLEASE HELP ME

THANKS A LOT

 

Hi,

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