Using for example an ODE like
ode = t^3 y''[t] + t y'[t] + y[t]
with the following boundary conditions
bc = {y[1] == 0, y'[1] == 1};
And using NDSolve, we have:
ti=1/100;
tf=1
sol = NDSolve[Flatten[{ode ==0, bc}],y,{t,ti,tf}]
We can see that t = 0 is an irregular singular point of ODE. And even using a high WorkingPrecision, PrecisionGoal, and AccuracyGoal, y[ti]
still being "wrong". What is the most efficient way to have a good solution close to t=0 using NDSolve?
I'm saying that it's wrong because defining the following function
testfunc[t_] = Log10[Abs[ode/.sol]]
We can see that testfunc[ti] = 29.827
when this needed to be close to 0.
DSolve[{ode == 0, bc}, y, t]
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