MATH
Exercise_Picard_sol.pdf

# Exercise_Picard_sol.pdf - Exercise 1 Write out the first...

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Exercise 1 Write out the first few terms of the Picard iteration for each of the following initial value problems. Where possible, find explicit solutions and describe the domain of this solution. (a) x 0 = x + 2; x (0) = 2 (b) x 0 = x 4 / 3 ; x (0) = 0 (c) x 0 = x 4 / 3 ; x (0) = 1 (d) x 0 = cos ( x ); x (0) = 0 (e) x 0 = 1 2 x ; x (1) = 1 Exercise 2 Consider the linear system X 0 = F ( X ) = 0 1 - 1 0 X, X (0) = (1 , 0) Find an analytical solution to the problem, and the first four terms in a Picard iteration. Exercise 3 Derive the Taylor series for

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