Find the sequence of Picard iterates for y2t y00SolutionThe

Find the sequence of Picard iterates for

y\'=2t

y(0)=0

Solution

The sequence of picard iterates can be calculated by using the formula

Phi(i+1) t = Phi(i)t + Integral ( 2sds) from 0 to t

Using the initial condition that Phi(0) t = 0, we get the value of Phi(1) t

Phi(1) t = 0 + Integral (2s ds) from 0 to t

=> s^2 from (0 to t)

=> t^2 - 0^2 = t^2

Phi(2) t = 0 + Integral (2s ds) from 0 to t

=> s^2 from (0 to t)

=> t^2 - 0^2 = t^2