MB86

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1 years, 9 days

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These are replies submitted by MB86

@Thomas Richard  Hi again, I tried to set the expansion point for series at infinity instead of 0 using

sols := dsolve(sys_ivp, vars, 'series', t = infinity)

but it didn't work and it gave me this error

Error, (in dsolve/SERIES) conflicting specifications of the series expansion point: 0 v.s. infinity

Not sure, but I guess this could be due to the fact that the initial conditions are defined at 0, while I'll try to use the series expansion at infinity. I keep trying different methods, but I thought I give an update on what I've tried so far.

@Thomas Richard Ideally, I would like to have a solution that works relatively well for all positive values of t. Even if it's not the exact solution, it's OK as long as the discrepency is accetptable and the approximated solution can predict the trend. No worries Thomas. I fully understand you must be very busy. You've been already very helpful. Thanks. I'll try to do more research about asymptotic expansion.

@Thomas Richard  Many thanks for your reply. The series solution is indeed a nice idea, but the only drawback is that it does not provide realistic results for large values of t. I am considering the possibility that, given there is no analytical solution for this system of ODEs, I can develop a semi-empirical solution in the form of f(t)exp(-t) + g(t)(1-exp(-t)), where f(t) represents the behavior at small values of t, and g(t) is the asymptotic behavior of the solution at large values of t. For f(t), I can use the series solution that you suggested, but is there any way I can find the asymptotic solution as t goes to infinity? Thanks in advance for taking the time to look into this.

@Kitonum Many thanks for your help. I was hoping to find an analytical solution, but thanks for sharing the numerical one. I was wondering if there is any way to find the asymptotic behaviour of variables x and y as t goes to infinity using the numerical solution. Please let me know if you have any insight on that.

@Preben Alsholm 

Thanks for your reply. That was useful.

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