# Ordinary Differential equation Successive Approximations

Ordinary Differential equation Successive Approximations

Taking $$\phi(0,\lambda)$$ as constant function, where it is equal to 0 which I consider as a first approximation, gives for the second approximation

$$\phi_1(t_1,\lambda)= \frac{sin(\sqrt\lambda)t}{\sqrt\lambda}$$

Nonetheless, when I try plugging this back into the integral equation I'm given two separable integrals with a q(s) term that I don't know how to integrate for the third approximation, do I just consider it to be q'(s)? Any help would be greatly appreciated.

• Can you also show us the algorithm to generate the approximations? – Sean Roberson Oct 7 '18 at 1:52