Hello,

I am trying to plot some movement equations, but the following error keeps happening:

Error, (in dsolve/numeric/process_input) system must be entered as a set/list of expressions/equations

when I tryed to rewrite the equation the error became:

Error, (in DEtools/convertsys) invalid specification of initial conditions

Can someone help me with those errors?

Here is the code:

restart;

with(LinearAlgebra);
with(linalg);
with(DifferentialGeometry);
with(VariationalCalculus);
with(Tensor);
with(tensor);
with(Tools);
DGsetup([t, x, y, z], M)

g1 := evalDG(N(t)^2*`&t`(dt, dt)-a(t)^2*(`&t`(dx, dx)+`&t`(dy, dy)+`&t`(dz, dz)))

g1inv := InverseMetric(g1)

C1 := Christoffel(g1)

RM1 := CurvatureTensor(C1)

RM1g := CurvatureTensor(g1)

ContractIndices(RM1, [[1, 3]])

ContractIndices(RM1g, [[1, 3]])

RT := RicciTensor(g1, RM1)

ContractIndices(RT, g1inv, [[1, 1], [2, 2]])

S1 := RicciScalar(g1, RM1)

ContractIndices(RT, g1inv, [[1, 1], [2, 2]])

RM1contra := RaiseLowerIndices(g1inv, RM1, [2, 3, 4])

RM1cov := RaiseLowerIndices(g1, RM1, [1])

Kret1 := ContractIndices(RM1contra, RM1cov, [[1, 1], [2, 2], [3, 3], [4, 4]])

eval(simplify(subs(N(t) = 1, Kret1)))

Lag := a(t)^3*N(t)*Kret1

phi = phi(t)

Lam := -(1/2)*a(t)^3*N(t)*((diff(phi, t))^2/N(t)^2+m^2*phi)

Ltot := Lag+Lam

EqELN := EulerLagrange(Ltot, t, N(t))

EqN := eval(simplify(subs(N(t) = 1, EqELN)))

Eqa := subs(N(t) = 1, Ltot)

EqELa := EulerLagrange(EqaD, t, a(t))

tini := 0

with(DEtools)

with(plots)

tfin = 10

(D(a))(tini) = 0

((D@@2)(a))(tini) = 0

((D@@3)(a))(tini) = 0

phi := a^-3

Dphi := 0

(D(N))(tini) = 0

((D@@2)(N))(tini) = 0

((D@@3)(N))(tini) = 0

sys1 := {EqN, a(tini) = 0.1e-2, (D(a))(tini) = 0.1e-2, ((D@@2)(a))(tini) = 0.1e-2, ((D@@3)(a))(tini) = 1}

tfin = 2

p1 := dsolve(sys1, type = numeric, abserr = 1.*10^(-8), relerr = 1.*10^(-8), range = tini .. tfin)

figN := odeplot(p1, [t, a(t)])

sys2 := {EqELa, a(tini) = 0.1e-6, (D(a))(tini) = 0.1e-4, ((D@@2)(a))(tini) = 0.1e-5, ((D@@3)(a))(tini) = 1, ((D@@4)(a))(tini) = 0.1e-5}

p2 := dsolve(sys2, type = numeric, abserr = 1.*10^(-8), relerr = 1.*10^(-8), range = tini .. tfin)

figa := odeplot(p2, [t, a(t)])

How do I plot the following with Maple 2015?

For my differential equations class we have to input the following problem into Maple, I've never used maple before and I was wondering if someone who is experienced with maple could help me out with the code to put into Maple. Thanks I appreciate it!

Using the Maple program, Write the procedure RungeKutta(f, a, b, aplpha, n) which use the improved Euler's method to approximate the solution of the initial-value problem y'=f(t,y), atb, y(a)= alpha at (n+1) equally spaced numbers in the interval [a,b]

The input parameters are as follow:

f is the name of the function f(t,y);

a and b are the end points of the interval of integration;

alpha is the initial condition.

The output: array w is the approximation of y at the (n+1) values of t.

Hi, 

I'm really not sure what else to say that isnt already obvious from the worksheet i uploaded, it's pretty obvious what i am trying to do i just dont understand what neutral operator even is, and couldn't find anything on the help page i was directed to by the error.

Download INVALID_NEUTRAL_OPERATOR.mw

I employed the sort command to sort through 10 solutions to a series of order 10.  However, I do not follow the logic of the output.  So I attempted to sort by ascending order by the magnitude, but I am getting errors which I am having trouble circumnavigating.  Can show me how to sort my solutions properly?

The worksheet is in my reply below.

restart;
with(PDEtools);
assume(k::real, x::real, omega::real, t::real, theta::real, c::real);
tr0 := c*(t*upsilon+x) = xi;
tr1 := I*(k*x+omega*t+theta);
tr2 := phi(lhs(tr0))*exp(tr1);
PDE := proc (u) options operator, arrow; I*(diff(u, t))+diff(u, x, x)-I*sigma*u*(conjugate(u)*(diff(u, x))-u*(diff(conjugate(u), x))) end proc;
Eq1 := PDE(tr2);
Eq2 := simplify(convert(expand(subs(tr0, Eq1)), diff));

for_maple_prime.mw

Hi, I'm currently studying the dynamics of a system of ODEs and I would like to plot a bifurcation diagram using Maple.

The system is:

.

Can anyone help me with a procedure to output a bifurcation diagram for the system?
Thanks.

Dear Users,

Recently, I started using Maple2017. In Maple 18, I have used the following commands for import/export and it worked fine.

Digits := 50;

Rhs:= ImportVector("/home/15_degree_3izto1_fixed/Vec.txt", source = delimited);

MatA:=ImportMatrix("/home/15_degree_3izto1_fixed/Mat.txt", source = delimited) ;

Note : Vec.txt contains float with 50 digits, and Mat.txt contains algebraic equation eg. 123456716798271394816*y+173974937*10^(-16)

While maple 18 used to import all the informations with 50 digits of accuracy, Maple2017 only import float[8] ?It only imports first 20 digits and so on..? What has changed in 2017?

Thanks and regards,

1.

with(Groebner):
K := {r-x^4,u-(x^3)*y,v-x*y^3,w-y^4};
G := Basis(K, 'tord', degrevlex(r,u,v,w));
R1 := eliminate(G, {r,u,v,w}); # eliminate is the reverse of Basis
Ga := Basis({a*G[1],a*G[2],a*G[3],a*G[4],a*G[5],a*G[6],a*G[7],a*G[8],a*G[9],a*G[10],a*G[11],a*G[12],a*G[13],a*G[14], (1-a)*K[1], (1-a)*K[2], (1-a)*K[3], (1-a)*K[4]}, 'tord', deglex(a,r,u,v,w));
Ga := remove(has, Ga, [x,y,a]);
eliminate(Ga, [r,u,v,w]);

how to eliminate Ga to find back K ?

2.

sol := eliminate({eq1,eq2,eq3,eq4},[x1,x2,x3,x4]);

with(Groebner):
K := {(rhs(sol[1][1])-lhs(sol[1][1])),(rhs(sol[1][2])-lhs(sol[1][2])),(rhs(sol[1][3])-lhs(sol[1][3])),(rhs(sol[1][4])-lhs(sol[1][4]))};
G := Basis(K, 'tord', degrevlex(x1,x2,x3,x4));
R1 := eliminate(G, {x1,x2,x3,x4}); # eliminate is the reverse of Basis
Ga := Basis({a*G[1],a*G[2],a*G[3],a*G[4], (1-a)*K[1], (1-a)*K[2], (1-a)*K[3], (1-a)*K[4]}, 'tord', deglex(a,x1,x2,x3,x4));
Ga := remove(has, Ga, [u1,u2,u3,u4,a]);

From Question1, is it possible to find from sol to eq1, eq2, eq3 and eq4 ?

restart;
with(PDEtools);
assume(k::real, x::real, omega::real, t::real, theta::real, c::real);
u := phi(c*(t*upsilon+x))*exp(I*(k*x+omega*t+theta));
PDE := proc (u) options operator, arrow; I*(diff(u, t))+diff(u, x, x)-I*sigma*u*(conjugate(u)*(diff(u, x))-u*conjugate(diff(u, x))) end proc;
Eq1 := PDE(u)

For example

if x*y*z+ x*y^2

after filter 

x*y*z

I have resolved the roots of a series both numerically & analytically.  Let me qualify numerical  versus analytical.  Analytically I evaluate the series without substituting values for the various parameters of the series.  I then differentiate the series, then substitute in the appropriate parametric values, & then solve.  By this method I obtained 5 complex roots.

The numerical approach has values already assigned to the parameters of the series.  I then differentiate & solve.  I obtain only REAL roots in this instance.  I then restricted these results to obtain the solution I believe to be correct given by result (7).

I cannot seem to steer the solver in the analytic case to obtain the correct REAL result that I am expecting.  Can anyone help on this?

Before any website moderator thinks this is the same question as Error-in-Isinternal-Too-Many-Levels, it is not.  I have resolved that question.  This is a different question, but on the same problem!

reconcile_solns.mw

hi, i have an expression "f" and i want to substitute the expression with Square root with another namee like phi, how should i do that? i should not use solve commands since the expression is more complicated and i have just pick part of it. tnx in advance.

 

Download problem.mw

Hi,

I tried a Animation with 10 randoms HeatMaps:

restart:

with(Statistics): with(LinearAlgebra); randomize(): with(plots):

f:= rand( 1..2 ):

for n to 10 do :
RM := Matrix(10, 10, proc (i, j) options operator, arrow; (-1)^f() end proc);
G[n] := HeatMap(RM, axis = [gridlines = [10, color = blue], thickness = 2]) ;
end do
display(seq(G[n], n = 1 .. 10), insequence = true);

But this is nor work as well. How do i this?

Regards.
 

Hello,

I want numerical randoms whose out are 1 or -1 only, how do i it?

I tried this:

with(Statistics):

RM := LinearAlgebra:-RandomMatrix(10, generator = -1 .. 1)

But this is not work as well.

Regards.