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umar khan

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8 years, 236 days
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These are replies submitted by umar khan

r should not be negative values...

umar khan 30
December 04 2016
0 0

@J4James 

r can't be negative the equation shows the graph of monotonic decreasing sequence.

@tomleslie  yes the solution is re...

umar khan 30
December 04 2016
0 0

@tomleslie 

yes the solution is real, and i also found the graph but did not understand how to get the value of r for which P(r) becomes 0.which maple command i should used to iterate P(r) till its become zero

system......

umar khan 30
December 04 2016
0 0

@Markiyan Hirnyk 

i use here cgs system, which is relevent to my problem. the vlaue of r may between 5*10^(5) to 15*10^(6).

that may be the write answer...

umar khan 30
December 04 2016
0 0

@Axel Vogt 

the system is in cgs and the required answer can be with in 5*10^(5) to 15*10^(6). and your answer lie in this range.

would you provide me the maple file also its graph

@Markiyan Hirnyk  all the data is ...

umar khan 30
December 04 2016
0 0

@Markiyan Hirnyk 

all the data is correct, this is 10^34 is not avagadro number. it is initiall value of pressure.

only one b.condition......

umar khan 30
December 02 2016
0 0

@Preben Alsholm 

ok, is it possible to satisfy the only  boundary condition w(688240)=-2.05684.if possile then kindly satisfy it. donot use v(0)=0

@J4James  ok i donot assign the va...

umar khan 30
December 02 2016
0 0

@J4James 

ok i donot assign the value of pi and neither use refresh command, but i need to find the solution of v(r) at that particular boundary, also v(r) is coupled with P(r). P(r) has decreasing graph form initial to final P=0.the behaviour of v(r) should be asymptotically flat as r increses. how so ever you use first whether v(r) or P(r). but please solve these.

@Preben Alsholm pi means 3.143and e...

umar khan 30
November 30 2016
0 2

@Preben Alsholm 

pi means 3.143

and exp(-v(r))

thanks for all your respons the below is...

umar khan 30
November 30 2016
0 3


 

> 

G := 6.6743*10^(-8); a := 1.9501*10^24; b := 1/3.025; c := 2.99792458*10^10; d := 2.035; pi := 3.143; g(r) = 1-omega(r)/(.1254); j(r) = e^(-(1/2)*v(r))*(1-2*G*M(r)/(r*c^2))^(1/2)

0.6674300000e-7

  

0.1950100000e25

  

.3305785124

  

0.2997924580e11

  

2.035

  

3.143

  

g(r) = 1-7.974481659*omega(r)

  

j(r) = e^(-(1/2)*v(r))*(1-0.1485232054e-27*M(r)/r)^(1/2)

 (1)
> 

ics := M(0) = 0, P(0) = 1.3668*10^34;

M(0) = 0, P(0) = 0.1366800000e35

 (2)
> 

conditions := v(0) = 0, "iterate it to find"*v(945215.73) = -.2425; 1; "v(r) is first ode but the two conditions should satisfy"

v(0) = 0, "iterate it to find"*v(945215.73) = -.2425

  

"v(r) is first ode but the two conditions should satisfy"

 (3)
> 

conditions := diff(g(r), r) = 0*"at", r = 0, "and"*g(945215.73) = 1-2*J(945215.73)/945215.73^3, "g(r) is 2 nd order ode in omega(r)"

-7.974481659*(diff(omega(r), r)) = 0, r = 0, "and"*(1-7.974481659*omega(945215.73)) = 1-0.2368302505e-17*J(945215.73), "g(r) is 2 nd order ode in omega(r)"

 (4)
> 

ics := J(0) = 0

J(0) = 0

 (5)
> 

diff(M(r), r) = 4*pi*r^2*(a*P(r)^b+P(r)/d)/c^2, diff(P(r), r) = -G*(a*P(r)^b+(1+d)*P(r)/d)*(M(r)+4*Pi*r^3*P(r)/c^2)/(c^2*(r^2-2*G*r*M(r)/c^2)), diff(v(r), r) = 1.485232054*10^(-28)*(M(r)+4.450600224*10^(-21)*Pi*r^3*P(r))/(r^2-1.485232054*10^(-28)*r*M(r)), diff(r^4*j(r)*(diff(g(r), r)), r)+Typesetting:-delayDotProduct(4*r^3*(diff(j(r), r)), g(r)) = 0, diff(J(r), r) = (8*pi*(1/3))*(a*P(r)^b+P(r)/d+P(r))*Typesetting:-delayDotProduct(f(r)*j(r), r^4)/(1-2*G*M(r)/(r*c^2))

diff(M(r), r) = 0.1398823650e-19*r^2*(0.1950100000e25*P(r)^.3305785124+.4914004914*P(r)), diff(P(r), r) = -0.7426160269e-28*(0.1950100000e25*P(r)^.3305785124+1.491400491*P(r))*(M(r)+0.4450600224e-20*Pi*r^3*P(r))/(r^2-0.1485232054e-27*r*M(r)), diff(v(r), r) = 0.1485232054e-27*(M(r)+0.4450600224e-20*Pi*r^3*P(r))/(r^2-0.1485232054e-27*r*M(r)), -31.89792664*r^3*e^(-(1/2)*v(r))*(1-0.1485232054e-27*M(r)/r)^(1/2)*(diff(omega(r), r))+3.987240830*r^4*e^(-(1/2)*v(r))*(diff(v(r), r))*ln(e)*(1-0.1485232054e-27*M(r)/r)^(1/2)*(diff(omega(r), r))-3.987240830*r^4*e^(-(1/2)*v(r))*(diff(omega(r), r))*(-0.1485232054e-27*(diff(M(r), r))/r+0.1485232054e-27*M(r)/r^2)/(1-0.1485232054e-27*M(r)/r)^(1/2)-7.974481659*r^4*e^(-(1/2)*v(r))*(1-0.1485232054e-27*M(r)/r)^(1/2)*(diff(diff(omega(r), r), r))+4*(r^3*(-(1/2)*e^(-(1/2)*v(r))*(diff(v(r), r))*ln(e)*(1-0.1485232054e-27*M(r)/r)^(1/2)+(1/2)*e^(-(1/2)*v(r))*(-0.1485232054e-27*(diff(M(r), r))/r+0.1485232054e-27*M(r)/r^2)/(1-0.1485232054e-27*M(r)/r)^(1/2)).(1-7.974481659*omega(r))) = 0, diff(J(r), r) = 8.381333333*(0.1950100000e25*P(r)^.3305785124+1.491400491*P(r))*(f(r)*e^(-(1/2)*v(r))*(1-0.1485232054e-27*M(r)/r)^(1/2).(r^4))/(1-0.1485232054e-27*M(r)/r)

 (6)
> 

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Download nonlinera_odes.mw

this is same problem in maple but just some change of dependent variables

in this file v(r) have two conditions i must satisfy v(945215.73) = -.2425 the other v(0)=0 may be satisfy.an other way to find the solution of v(r) at v(0)=0 and iterate it to find v(945215.73) = -0.2425.I found an incresing graph of v(r) but it does not satisty v(945215.73) = -.2425.

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