How to calculate it nurmerically?

How to calculate it nurmerically?

@MapleFans001 

How to calculate it numerically?

@MapleFans001 

How to calculate it numerically?

Thank you. It's my first time to know the existence of exponential integral.

Thank you. It's my first time to know the existence of exponential integral.

setting x(0) = 10, theta(0) = 20

can see graph it is symmetric

How to set good initial ? actually i do not know the meaning of value set as initial

setting x(0) = 10, theta(0) = 20

can see graph it is symmetric

How to set good initial ? actually i do not know the meaning of value set as initial

When meeting can not evaluate solution further left of .2 probabaly singularity.

How to change initial to prevent singularity to plot graph successfully?

if there is a procedure to deal with this situation, hope that deal with next time meet this case again

When meeting can not evaluate solution further left of .2 probabaly singularity.

How to change initial to prevent singularity to plot graph successfully?

if there is a procedure to deal with this situation, hope that deal with next time meet this case again

@MapleFans001 

sometimes i meet

proc(x_rkf45)  ...  end;
Warning, cannot evaluate the solution further right of .66929842, probably a singularity

@MapleFans001 

sometimes i meet

proc(x_rkf45)  ...  end;
Warning, cannot evaluate the solution further right of .66929842, probably a singularity

@Preben Alsholm 

now it can be solved without changing the equations

ex1 := {
Diff(f1(t), t$2)
+ 2*(-G*M/(r*(-r*c^2+2*G*M)))*Diff(f1(t), t)*Diff(f2(t), t) = 0,

Diff(f2(t), t$2)
+ (-(-r*c^2+2*G*M)*G*M/(r^3*c^2))*Diff(f1(t), t)^2
+ (G*M/(r*(-r*c^2+2*G*M)))*Diff(f2(t), t$2)
+ ((-r*c^2+2*G*M)/c^2)*Diff(f3(t), t$2)
+ ((-r*c^2+2*G*M)*sin(theta)^2/c^2)*Diff(f4(t), t)^2 = 0,

Diff(f3(t), t$2)
+ 2*(1/r)*Diff(f2(t), t)*Diff(f3(t), t)
+ (-sin(theta)*cos(theta))*Diff(f4(t), t)^2 = 0,

Diff(f4(t), t$2)
+ 2*(1/r)*Diff(f2(t), t)*Diff(f4(t), t)
+ 2*(cos(theta)/sin(theta))*Diff(f3(t), t)*Diff(f4(t), t) = 0

};

@Preben Alsholm 

now it can be solved without changing the equations

ex1 := {
Diff(f1(t), t$2)
+ 2*(-G*M/(r*(-r*c^2+2*G*M)))*Diff(f1(t), t)*Diff(f2(t), t) = 0,

Diff(f2(t), t$2)
+ (-(-r*c^2+2*G*M)*G*M/(r^3*c^2))*Diff(f1(t), t)^2
+ (G*M/(r*(-r*c^2+2*G*M)))*Diff(f2(t), t$2)
+ ((-r*c^2+2*G*M)/c^2)*Diff(f3(t), t$2)
+ ((-r*c^2+2*G*M)*sin(theta)^2/c^2)*Diff(f4(t), t)^2 = 0,

Diff(f3(t), t$2)
+ 2*(1/r)*Diff(f2(t), t)*Diff(f3(t), t)
+ (-sin(theta)*cos(theta))*Diff(f4(t), t)^2 = 0,

Diff(f4(t), t$2)
+ 2*(1/r)*Diff(f2(t), t)*Diff(f4(t), t)
+ 2*(cos(theta)/sin(theta))*Diff(f3(t), t)*Diff(f4(t), t) = 0

};

if i change to what you say,

> dsol := dsolve(`union`(ex1, ic), numeric);
proc(x_rkf45)  ...  end;

How to show dsol? And how to odeplot this? And how to phaseportrait this?

> odeplot(dsol, [t, f(t)], 0 .. 100);
Error, (in plots/odeplot) curve is not fully specified in terms of the ODE solution, found additional unknowns {f(t)}