Step 3 – Substitute fory(t) in the integrandas above:
Step 4 – Substitute fory(t) in the integrandas donepreviously:
Thus,the initialfour functionsin the sequencedefinedby Picard’s methodare:
The methodalso statesthat this sequencewill convergeto the solutiony(x) of the initialvalueproblem,i.e.
A patternof the functionsin the sequenceYn(x) is emergingbut it is not an obviousone. We do knowY
n(x) will convergeto the solutionfor this problemby Picard’s method.The exactsolutionfor this problem
can be calculatedand is givenby: