Apply the successive approximation formula to compute yn(x) for n ≤ 4. Then write the exponential series for which these approximations are partial sums dy/dx = 4x(y+2x2) , y(0) = 0
Apply the successive approximation formula to compute yn(x) for n ≤ 4. Then write the exponential series for which these approximations are partial sums dy/dx = 4x(y+2x2) , y(0) = 0
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.5: Iterative Methods For Solving Linear Systems
Problem 20EQ
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Question
Apply the successive approximation formula to compute yn(x) for n ≤ 4. Then write the exponential series for which these approximations are partial sums
dy/dx = 4x(y+2x2) , y(0) = 0
Expert Solution
Step 1
Given- The IVP is-
Method Used-
Picard's method of successive approximation:
(1)
Since,
Then, the equation (1) becomes
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