From a cubic function where y(0)=1, y(1)=0, and where there is a local max at y(5/13) I created a basic separable differential equation problem. I wanted to analyze how well different ordered Runge Kutta methods works in an interval [0,1]. Here it is:(adsbygoogle = window.adsbygoogle || []).push({});

dy/dt=-6(6/13)^{1/3}(y-343/468)^{2/3}, y(0)=1

This ODE yields the cubic solution of

y=1/468(-12t+5)^{3}+343/468

Now it is clear that y(1)=0

But using the several Runge Kutta programs with various computer software (mathematica, ti-nspire cas, mathstudio, etc.) yields a complex solutions for y(1). For example, using the classical RK4 with h=.1 yields

y(1)=0.718779+.005811i.

I don't see how the programs get a complex solution when all the functions have no even roots. Does anyone what is going on with these programs?

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# A basic ODE where Runge Kutta doesn't work?

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