Items tagged with numeric numeric Tagged Items Feed

of the improper integral of exp((1-x)/((1-x)^2+y^2)) over the unit disk x^2+y^2 <= 1 with Maple? For purists the function is assumed to be undefined at (1,0). It is not so difficult to verify that statement  by hand. It is not easy to prove that with Maple.

My try was

f := evalc(exp(Re(1/(1-x-I*y))));


VectorCalculus:-int(f, [x, y] = Circle(`<,>`(0, 0), 1), numeric);

and

evalf(Int(f, [y = -sqrt(-x^2+1) .. sqrt(-x^2+1), x = -1 .. 1]));
.

Edit. The formula for f.                  

PS.

 

 

 

Could anyone please hepl me? I have the following system

e1 := exp(F(r)/phi_0)*L*A(r) = (1/2)*(2*(diff(A(r), r, r))*B(r)*A(r)*r*C(r)+2*B(r)*A(r)*(diff(A(r), r))*(diff(C(r), r))*r-(diff(A(r), r))^2*B(r)*r*C(r)-(diff(A(r), r))*(diff(B(r), r))*A(r)*r*C(r)+4*B(r)*A(r)*(diff(A(r), r))*C(r))/(B(r)^2*A(r)*r*C(r));
e2 := alpha*(diff(F(r), r, r))+(alpha^2+omega)*(diff(F(r), r))^2+(1/4)*(4*(diff(C(r), r, r))*B(r)*A(r)^2*C(r)*r+2*(diff(A(r), r, r))*A(r)*B(r)*r*C(r)^2-2*B(r)*A(r)^2*(diff(C(r), r))^2*r-(diff(A(r), r))^2*B(r)*r*C(r)^2-2*A(r)^2*C(r)*(diff(C(r), r))*(diff(B(r), r))*r-(diff(A(r), r))*(diff(B(r), r))*A(r)*r*C(r)^2+8*B(r)*A(r)^2*C(r)*(diff(C(r), r))-4*A(r)^2*C(r)^2*(diff(B(r), r)))/(r*A(r)^2*B(r)*C(r)^2)-(1/4)*(2*(diff(A(r), r, r))*B(r)*A(r)*r*C(r)+2*B(r)*A(r)*(diff(A(r), r))*(diff(C(r), r))*r-(diff(A(r), r))^2*B(r)*r*C(r)-(diff(A(r), r))*(diff(B(r), r))*A(r)*r*C(r)+4*B(r)*A(r)*(diff(A(r), r))*C(r))/(B(r)*A(r)^2*r*C(r)) = 0;
e3 := (1/4)*(-2*(diff(C(r), r, r))*B(r)*A(r)*r^2-B(r)*(diff(A(r), r))*(diff(C(r), r))*r^2+A(r)*(diff(C(r), r))*(diff(B(r), r))*r^2-8*B(r)*A(r)*(diff(C(r), r))*r-2*B(r)*(diff(A(r), r))*C(r)*r+2*A(r)*C(r)*(diff(B(r), r))*r+4*B(r)^2*A(r)-4*B(r)*A(r)*C(r))/(B(r)^2*A(r)) = -(1/4)*(2*(diff(A(r), r, r))*B(r)*A(r)*r*C(r)+2*B(r)*A(r)*(diff(A(r), r))*(diff(C(r), r))*r-(diff(A(r), r))^2*B(r)*r*C(r)-(diff(A(r), r))*(diff(B(r), r))*A(r)*r*C(r)+4*B(r)*A(r)*(diff(A(r), r))*C(r))*r/(B(r)^2*A(r)^2);
e4 := -(alpha^2+2*omega)*(diff(F(r), r))*(-(1/2)*(-(diff(A(r), r))*B(r)*r^4*C(r)^2-A(r)*(diff(B(r), r))*r^4*C(r)^2-4*A(r)*B(r)*r^3*C(r)^2-2*A(r)*B(r)*r^4*C(r)*(diff(C(r), r)))/(A(r)*B(r)*r^4*C(r)^2)-(diff(B(r), r))/B(r)+(diff(F(r), r, r))/(diff(F(r), r))+alpha*(diff(F(r), r)))/B(r) = -exp(F(r)/phi_0)*V_0*(alpha-1/phi_0);

phi_0 := -alpha/(2*alpha^2+2*omega); L := V_0*(1-(alpha-1/phi_0)*alpha/(3*alpha^2+2*omega)); V_0 := -lambda*exp(-fc/phi_0); fc := ln((4*alpha^2+2*omega)/(G_0*(3*alpha^2+2*omega)))/alpha; m := (2/(1+g))^(1/2); n := g*(2/(1+g))^(1/2); P := (G_0*(3*alpha^2+2*omega)/(4*alpha^2+2*omega))^(-2*alpha/(n-m)); eta := 1.4*G_0*Ms*(2/(1+g))^(-1/2)/c^2; g := 1-alpha^2/(2*alpha^2+omega);

omega := -10^5; alpha := 1; G_0 := 6.67*10^(-11); lambda := 10^(-52); c := 2.9*10^8; Ms := 1.9*10^30;
ri := evalf(1000*eta);

ics := A(2.109660445*10^6) = 1, (D(A))(2.109660445*10^6) = 2.370091128*10^(-15)*sqrt(2)*sqrt(99998)*sqrt(199997), B(2.109660445*10^6) = 1, C(2.109660445*10^6) = 1, (D(C))(2.109660445*10^6) = 4.740182256*10^(-15)*(1-(99999/19999300006)*sqrt(2)*sqrt(99998)*sqrt(199997))*(1-1.000017501*10^(-8)*sqrt(2)*sqrt(99998)*sqrt(199997))^(-(99999/19999300006)*sqrt(2)*sqrt(99998)*sqrt(199997))*sqrt(2)*sqrt(99998)*sqrt(199997), f(2.109660445*10^6) = 23.43081116, (D(f))(2.109660445*10^6) = 4.749681180*10^(-15):

eta:=2109.660445: sys:=e1,e2,e3,e4; vars:=[A(r),B(r),C(r),F(r)];

dsn3 := dsolve([sys, ics], numeric, vars, range = 3*eta .. 50*eta);

Results in

Warning, cannot evaluate the solution past the initial point, problem may be complex, initially singular or improperly set up

Setting f(r)=Const,V_0=0 which is a physically relevant case, results in

Error, (in simplify/normal) numeric exception: division by zero

I suugest the problem is that the equation contain sqared derivatives, hence there are several solution branches corresponding to different signs of square root. Maple chooses the singular branch. How can I force it to choose another branch or calculete all of them?

Thanks in advance..





This is the simplest method to explain numerically solving an ODE, more precisely, an IVP.

Using the method, to get a fell for numerics as well as for the nature of IVPs, solve the IVP numerically with a PC, 10steps.

Graph the computed values and the solution curve on the same coordinate axes.

 

y'=(y-x)^2, y(0)=0 , h=0.1

Sol. y=x-tanh(x)

 

I don't know well maple. 

I study Advanced Engineering Math and using maple, but i am stopped in this test.

I want to know how solve this problem.

please teach me~ 

IT IS EULER's method

Hi there. I'm Student

i want to know how solve this problem.

please teach me! 

y'=(y-x)^2, y(0)=0, h=0.1

sol.y=x-tanh(x)

how solve this problem for maple? 

please teach me~

Dear all,

I have a question regarding the dsolve procedure in Maple. I'm trying to construct a neutron star model using the Tolman-Oppenheimer-Volkoff equation using a polytropic equation of state (EOS) which requires me to solve the ode system:

diff(rho(r),r)=-(rho(r)*(1+K/(5/3-1)*rho(r)^(5/3-1))+K*rho(r)^(5/3))*(4*Pi*r^3*K*rho(r)^(5/3)+m(r))/(K*5/3*rho(r)^(5/3-1)*r*(r-2*m(r)))

diff(m(r),r)=4*Pi*rho(r)*(1+K/(5/3-1)*rho(r)^(5/3-1)

where I have used the EOS P(r)=K*rho(r)^(5/3) and K is a known constant. rho is the density of the star, m it's mass and P the pressure inside the star.

For the initial conditions I have chosen: rho(10^(-10))=rho_0 and m(10^-10)=0. I have chosen r=10^-10 as the innermost point for the integration, since the differential equation for rho is singular at r=0. rho_0 is the central density of the star.

I solve these equations numerically using:

TOV:=dsolve({ode,ics},numeric,output=listprocedure)

where ode is my system of differential equations and ics are my initial conditions. I need now the radius of the star (R_star), which is the maximum value of r, up until which Maple has carried out the integration.

My problem is, I don't know of any efficient way, to do this. What I'm doing currently is defining a procedure TOVr:=rhs(TOV[1]) and I evaluate it at a very high value of r, for which Maple returns me the error message: "Error, (in TOVr) cannot evaluate the solution further right of ..., probably a singularity". I then use the command TOVr('last') to call the maximum value of r and to store it.

I can use the above method, as long as I'm solving the ODEs only for a few different values of rho_0. But I would like to plot m(R_star) for values of rho_0 ranging from 10^(-14) to 10^(-12) in order to find the value of rho_0, for which I can obtain the maximum value for m(R_star). But this requires me to know the value of R_star for every rho_0 and using the above method is not feasible for say hundred different values of rho_0, since I can't write a loop, because it get's terminated as soon as Maple gives me the first error message.

I was thinking of using perhaps the 'events' command in dsolve, to stop the numeric integration once the value for the pressure drops very low, say below 10^(-46), since the radius at which P(r)=0 defines the stellar surface. I tried using:

TOV:=dsolve({ode,ics},numeric, events=[[K*rho(r)^(5/3)-10^(-46),halt]])

but if I try again to evaluate the solution at a large value of r, I get the above error message, and the integration doesn't get canceled, although the value 10^(-46) is bigger than the value for the pressure I would obtain for R_star using TOVr('last') and Maple shouldn't encounter a singularity.

Am I using the 'events' command wrong? And does somebody know of a more efficient method to obtain the maximum value of a variable after carying out a numerical integration using dsolve?

Sorry for the long post and thank you all.

So i got a procedure test, she is kind of numeric, i whant to optimaze test([.5, .5, .5], 1, 3, 100, 100, true, [x, 0, 0, 0, 0])=0 by x. But optinization substitutes x like a symbol, i tryed all methods but they all do the same.

f := proc (x) options operator, arrow; abs(test([.5, .5, .5], 1, 3, 100, 100, true, [x, 0, 0, 0, 0])-.4) end proc; Minimize(f(x));
%;
Error, (in test) cannot determine if this expression is true or false: 0 < -43.0+100*x


Can i some how use optinization on such procedure?

file link  - >    primset.mw

I've got the following four differential equations :

v_x:=diff(x(t),t);
v_y:=diff(y(t),t);
d2v_x:=-((C_d)*rho*Pi*(r^2)*(v_x)*sqrt((v_x)^2 +(v_y)^2))/(2*m);
d2v_y:=-((C_d)*rho*Pi*(r^2)*(v_y)*sqrt((v_x)^2 +(v_y)^2))/(2*m)-g;


and the following initial value conditions:

x(0)=0,y(0)=0,v_x(0)=v0/sqrt(2),v_y(0)=v0/sqrt(2) given v0=65 

I need to solve these using the numeric type and then draw overlaid plots

(i) setting C_d=0

(ii) leaving C_d as a variable

before plotting y(t) vs x(t). The hint for this last part is that the path can be seeing using [x(t),y(t)] instead of [t,y(t)]

I've tried to do it but seemed to have several syntax errors.

 

 

I've got the following diff.eq

y'(x)=sin(x*y(x)) given y(0)=1 

and need to solve it numerically which is why I've used:

dy4:=diff(y(x),x);
eqn4:=dy4=sin(x*y(x));
ic1:=y(0)=1;
ans3:=dsolve({eqn4,ic1},y(x),type=numeric);

This code doesn't return a value though and in fact, ans3 is being displayed as a procedure

"ans3:=proc(x_rkf45) ... end proc"

I don't quite understand why and what I need to do to get the required numerical solution

 

Hello,

I have a little problem. I have a system of ODEs, I can solve (with numeric solve) it but I can't plot it...
Any idea to help ?

Thank you !!

Here is my code:

with(DEtools);
beta := 1; lambda := 5; nu := 1; Delta := 1;


sys := {C(0) = 0, In(0) = .2, diff(C(u), u) = beta*In(u)*s(u)-C(u)/nu, diff(In(u), u) = C(u)/nu-In(u)/lambda+Delta*(diff(diff(In(u), u), u)), diff(s(u), u) = -beta*In(u)*s(u), s(0) = .8, (D(In))(0) = .2}

dsys := dsolve(sys, numeric, [In(u), s(u), C(u)])

plot(dsys[1], u = 0 .. .5, axes = boxed)

And I have this error:

Warning, expecting only range variable u in expression dsys[1] to be plotted but found name dsys[1]


PS: Maple solves the system without any problem:

 dsys(.5);


        [                                              
        [u = 0.5, In(u) = HFloat(0.33305297276372425),
        [                                              

           d                                       
          --- In(u) = HFloat(0.33950703755414946),
           du                                      

          s(u) = HFloat(0.7022184797811994),

                                           ]
          C(u) = HFloat(0.0781621551198558)]
                                           ]

Good day everyone, how can one check for the congence of numerical solution of this ODE in maple? See it here 1.mw

Best regards.

How to numerically solve the problem

with Maple? Such type problems arise in elasticity theory (for example, see https://zbmath.org/?q=an:01366371).

Edit. Typo in the code:sin(y(x)) instead of sin(x).

 

I need to plot the maximum of x^2 and sqrt(|x|) together on one graph. I've currently defined a procedure f that uses an if-else construct for the given function. However, when I use plot(f,-3..3); I get the following error:

"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"

How do I resolve this error?

 

I am currently running into an issue where the numerical solution to an equation (involving an integral, yes, but the value I am solving for is simly a constant in the integral) is taking significantly longer than I would hope it would to solve. I am solving a similar equation (with a simpler expression) and it is significantly easier to solve, and I am hoping for that kind of speed.

On the last two lines in the attachment, I have two expressions. The penultimate expression is the baseline speed that I would like to match. The last expression is the fsolve I would like to speed up.

Is there any way to numerically speed up the process? I found that when I did tracelast after halting the process, there were HUGE numbers being added and subtracted, multiplied and divided. Not only did this significantly slow down the proecss but it also adds much numerical instability, which I would also like to avoid.

All help would be appreciated.

pole-dragging-mapleprimes.mw

Hi, all

I use INT to calculate multiple integration as below. It runs more than 20 hours without results. I wander is there any problem in my codes.

restart;
A := sin(k*Pi*(x-h*cos(theta))/a)*sin(l*Pi*(y-h*sin(theta))/b)*sin(k[0]*h)*sin(k*Pi*x/a)*sin(l*Pi*y/b);

W := evalf[5](int(int(int(int(A, h = 0 .. (x-a)/cos(theta)), theta = Pi+arctan((b-y)/(a-x)) .. 3*Pi*(1/2)), x = 0 .. a), y = 0 .. b, numeric))

 

Thanks

hi...plese help me

:

how i can solve set of non linear differential equation with a unknown parameter with numeric role in maple software??

thank a lot ...

1 2 3 4 5 6 7 Last Page 1 of 15