Maple 18 Questions and Posts

These are Posts and Questions associated with the product, Maple 18

Dear maple users,
Greetings.
How to plot residual error for BVP.
Here I have enclosed the file.rerror.mw
 

restart; with(plots)

fcns := {f(eta), g(eta)}:

bet := 0.:

eq1 := diff(f(eta), `$`(eta, 3))+(diff(f(eta), `$`(eta, 2)))*f(eta)+be*((diff(g(eta), `$`(eta, 1)))^2-(diff(g(eta), `$`(eta, 2)))*g(eta)) = 0:

eq2 := pr*lam*(diff(g(eta), `$`(eta, 3)))+(diff(g(eta), `$`(eta, 2)))*f(eta)-(diff(f(eta), `$`(eta, 2)))*g(eta) = 0:

bc := f(0) = 0, (D(f))(0) = 0, (D(f))(N) = 1, g(0) = 0, ((D@@2)(g))(0) = 0, (D(g))(N) = 1;

f(0) = 0, (D(f))(0) = 0, (D(f))(5) = 1, g(0) = 0, ((D@@2)(g))(0) = 0, (D(g))(5) = 1

(1)

R := dsolve(eval({bc, eq1, eq2}), fcns, type = numeric, method = bvp[midrich], output = listprocedure):

Sol_exact := dsolve(eval({bc, eq1, eq2}), fcns):

``


 

Download rerror.mw

Have a good day

 

Dear all

I need your help to compute the discrete convolution product. Is there a simple way in maple that hep me to compute the coefficient of the matrix g 

thanks

convolution.mw

 

 

restart;
solve({l*(2*l^2*lambda^4*sigma*w*a[2]+l^2*lambda^2*mu*w*b[1]+6*l*lambda^2*m*sigma*a[0]^2-6*l*lambda^2*m*b[1]^2+6*l*m*mu^2*a[0]^2-l*lambda^2*rho*sigma*a[0]-l*mu^2*rho*a[0]+4*lambda^2*sigma*w*a[0]+4*mu^2*w*a[0]) = 0, l*(2*l^2*lambda^3*sigma*w*a[1]+6*l^2*lambda^2*mu*w*b[2]+2*l^2*lambda*mu^2*w*a[1]+12*l*lambda^2*m*sigma*a[0]*a[1]-12*l*lambda^2*m*b[1]*b[2]-l*lambda^2*rho*sigma*a[1]+12*l*m*mu^2*a[0]*a[1]-l*mu^2*rho*a[1]+4*lambda^2*sigma*w*a[1]+4*mu^2*w*a[1]) = 0, l*(5*l^2*lambda^3*sigma*w*b[2]-3*l^2*lambda^2*mu*sigma*w*a[1]-7*l^2*lambda*mu^2*w*b[2]-3*l^2*mu^3*w*a[1]+12*l*lambda^2*m*sigma*a[0]*b[2]+12*l*lambda^2*m*sigma*a[1]*b[1]-l*lambda^2*rho*sigma*b[2]+24*l*lambda*m*mu*b[1]*b[2]+12*l*m*mu^2*a[0]*b[2]+12*l*m*mu^2*a[1]*b[1]-l*mu^2*rho*b[2]+4*lambda^2*sigma*w*b[2]+4*mu^2*w*b[2]) = 0, l*(8*l^2*lambda^3*sigma*w*a[2]+6*l^2*lambda*mu^2*w*a[2]+12*l*lambda^2*m*sigma*a[0]*a[2]+6*l*lambda^2*m*sigma*a[1]^2+l^2*lambda*mu*w*b[1]-6*l*lambda^2*m*b[2]^2-l*lambda^2*rho*sigma*a[2]+12*l*m*mu^2*a[0]*a[2]+6*l*m*mu^2*a[1]^2-6*l*lambda*m*b[1]^2-l*mu^2*rho*a[2]+4*lambda^2*sigma*w*a[2]+4*mu^2*w*a[2]) = 0, -l*(4*l^2*lambda^3*mu*sigma*w*a[2]-l^2*lambda^3*sigma*w*b[1]+l^2*lambda*mu^2*w*b[1]-12*l*lambda^2*m*sigma*a[0]*b[1]+l*lambda^2*rho*sigma*b[1]-12*l*lambda*m*mu*b[1]^2-12*l*m*mu^2*a[0]*b[1]+l*mu^2*rho*b[1]-4*lambda^2*sigma*w*b[1]-4*mu^2*w*b[1]) = 0, 6*l^2*(l*lambda^2*sigma*w*a[2]+lambda^2*m*sigma*a[2]^2+l*mu^2*w*a[2]+m*mu^2*a[2]^2-lambda*m*b[2]^2) = 0, 2*l^2*(l*lambda^2*sigma*w*a[1]+6*lambda^2*m*sigma*a[1]*a[2]+3*l*lambda*mu*w*b[2]+l*mu^2*w*a[1]+6*m*mu^2*a[1]*a[2]-6*lambda*m*b[1]*b[2]) = 0, -2*l^2*(5*l*lambda^2*mu*sigma*w*a[2]-l*lambda^2*sigma*w*b[1]+5*l*mu^3*w*a[2]-6*lambda^2*m*sigma*a[1]*b[2]-6*lambda^2*m*sigma*a[2]*b[1]-l*mu^2*w*b[1]-6*lambda*m*mu*b[2]^2-6*m*mu^2*a[1]*b[2]-6*m*mu^2*a[2]*b[1]) = 0, 6*l^2*b[2]*(l*w+2*m*a[2]) = 0}, {a[0], a[1], a[2], b[1], b[2]});
Warning, solutions may have been lost
{a[0] = 0, a[1] = 0, a[2] = 0, b[1] = 0, b[2] = 0}, 

   /       l rho - 4 w                                        \ 
  { a[0] = -----------, a[1] = 0, a[2] = 0, b[1] = 0, b[2] = 0 }
   \          6 l m                                           / 
 

Dear friends, please I would like to ask for your help with the following situation: 

Suppose I have an Array   A:=Array([4]);   and I have to take the element A[i], add 1 to it and then append it to A, with i = 1..3. The result would be, 

A:= [4 5 6 7] 

I do know how to perform the task with a for loop, however I know that for large i it is more advisable to use seq for speed reasons.   I cannot find the right syntax to perform such a task with seq. Could you please advise me how to do so? 

Many thanks for your help. 

Dear all

I have data and a vector d. 
I would like to sum the elements of the vector d corresponding to the index  of the element data <=0.01 

Step 1: we select the index of data that corresponds to data<=0.01

step 2: we select the consecutive index corresponding to data<=0.01

Step 3 : we sum the element of d corresponding to the previous index

step 4: update d=d/number(index) ;

Please see my attached code. It's done by hand how can reformulate the code.

 

 

code_vector.mw

many thanks

 

I keep getting errors empty sets or only header information using the HTTP or URL package to when trying to download files from here through Maple. 

How do I download the csv files from here?
https://github.com/CSSEGISandData/COVID-19/tree/master/csse_covid_19_data/csse_covid_19_time_series

 

How do I know that what numerical method has maple used in this code.?

dsolve({eq11,eq21,eq3,eq4,bc21,bc22},numeric,continuation=lambda1,maxmesh=15000, output=array([seq( i, i=0..N,0.01 )]))

 

     Dear Sir/Madam,

I have faced a problem while using Maple 18. The  warning is the following

Warning, The use of global variables in numerical ODE problems is deprecated, and will be removed in a future release. Use the 'parameters' argument instead (see ?dsolve,numeric,parameters)

This is the code

restart;
with(plots);
beta := 0.2e-1; delta := .5; PI := 10000; mu := 0.16e-1; tau := 0.3e-1; rho := 0.4e-1; epsilon := 0.4e-1; sigma[1] := 0.1e-2; sigma[2] := 0.2e-2; eta := 0.6e-1;
sys := {diff(e(t), t) = beta*(sigma[1]*i(t)+sigma[2]*e(t))*s(t)-(delta+mu)*e(t), diff(i(t), t) = tau*delta*e(t)-(epsilon+rho+mu)*i*t, diff(r(t), t) = (1-tau)*delta*e(t)+epsilon*i(t)-(mu+eta)*r(t), diff(s(t), t) = PI+eta*r(t)-beta*(sigma[1]*i(t)+sigma[2]*e(t))*s(t)-mu*s(t), e(0) = 148, i(0) = 74, r(0) = 14, s(0) = 4110};
p1 := dsolve(sys, numeric, method = rkf45, output = procedurelist);
Warning, The use of global variables in numerical ODE problems is deprecated, and will be removed in a future release. Use the 'parameters' argument instead (see ?dsolve,numeric,parameters)
Error, (in dsolve/numeric) i(t) and i cannot both appear in the given ODE
p2o := odeplot(p1, [t, s(t)], 0 .. 4, numpoints = 100, labels = ["Time (months)", " Infected  "], labeldirections = [horizontal, vertical], style = line, color = red, axes = boxed);
Error, (in plots/odeplot) input is not a valid dsolve/numeric solution

plots[display](p2o);

 

Maple Worksheet - Error

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

Download nnn.mw

If we have an equation for the generalized Bloch sphere i.e.,

\partial_{t}(u^{2} + v^{2} + w^{2}) = 0,

where u, v and w are functions of x and t and the initial conditions u=v=0, w=-1. Then how to plot this equation on maple?

Dear all

I applied the definition of a permutation matrix to a given matrix A to obtain a Tridiagonal Toeplitz matrix, but I haven't any idea why the final result looks strange.

Permutation_matrix.mw

 

 

Many thanks

 

 

Dear all

Using maple I can't obtain an exact solution, my goal for which initial condition can the solution diverge to infinity if maple can not give us a solution.

special_condition_diverge.mw

many thanks

 

Dear all

I would like to compute a Laurent of a given function at an isolated point.

laurent_series.mw

thanks for your help

Dear all

I would like to solve a linear system A X=b whee A is a matrix n times n

If A is a tri-diagonal matrix, how can we write simple code to make A upper-triangular and then we solve the system using backward substitution

many thanks

 

I am trying to simplify an expression, and leave W in terms of other variables. But unfortunately I can't delete the RootOf, and I can't see the expressions. Could you please help me.

 

 

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