Hello, I am doing a Taylor expansion of the classical fourth order Runge- Kutta method. The formula looks like
y[n+1] = y[n] + h/6 * (k_1 + 2*k_2 + 2*k_3 + k_4) To do the expansion, I have to expand k_1, k_2, k_3, and k_4, where k_n +1 is a function of k_n. Doing a Taylor expansion of k_2 is simple. Then I take that expansion and use it in the expansion for k_3, which is more complicated. Finally, I take the expression for k_3 and plug into the expansion for k_4, which is now quite large. Since I only care about terms with powers of h less than 5, is there a way that I can quickly kill the high h powers? For k_3, I used the polys.Poly class method coeff() to get the coefficients for the lower powers of h, but this method is proving to be too slow for k_4. Does anyone have suggestions for alternatives to try? Hopefully there is something obvious I'm missing. I'm a relative newcomer to sympy. Thanks in advance, Josh -- You received this message because you are subscribed to the Google Groups "sympy" group. To post to this group, send email to [email protected]. To unsubscribe from this group, send email to [email protected]. For more options, visit this group at http://groups.google.com/group/sympy?hl=en.
