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
icon
Related questions
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-

dydx=4xy+2x2,   y(0)=0

 

Method Used- 

Picard's method of successive approximation:

yk+1=y0+x0xfx,ykdx      (1)

Since, x0=0

Then, the equation (1) becomes

yk+1=y0+0xfx,ykdx

steps

Step by step

Solved in 2 steps

Blurred answer
Knowledge Booster
Power Series
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning