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Consider the 1st order initial value problem: y' = f(t, y), 0sts2, y(0) = yo A certain method is used to solve the IVP, the truncation error of this method has the form: k,h? + k,h* + kzh6 + . An approximation of y(1) using this method with h = 0.2 and h = 0.1 are respectively 1.3 and 1.4. Using Richardson's extrapolation to improve the approximation value of y(1), we obtain: 0.75 1.5 1.4333 0.5

Consider the 1st order initial value problem: y' = f(t, y), 0sts2, y(0) = yo A certain method is used to solve the IVP, the truncation error of this method has the form: k,h? + k,h* + kzh6 + . An approximation of y(1) using this method with h = 0.2 and h = 0.1 are respectively 1.3 and 1.4. Using Richardson's extrapolation to improve the approximation value of y(1), we obtain: 0.75 1.5 1.4333 0.5

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Consider the 1st order initial value problem: y' = f(t,y), 0sts2, y(0) = yo A certain method is used to solve the IVP, the truncation error of this method has the form: k, h? + k,h* + k3h6 + ... An approximation of y(1) using this method with h = 0.2 and h = 0.1 are respectively 1.3 and 1.4. Using Richardson's extrapolation to improve the approximation value of y(1), we obtain: 0.75 1.5 1.4333 0.5
Transcribed Image Text:Consider the 1st order initial value problem: y' = f(t,y), 0sts2, y(0) = yo A certain method is used to solve the IVP, the truncation error of this method has the form: k, h? + k,h* + k3h6 + ... An approximation of y(1) using this method with h = 0.2 and h = 0.1 are respectively 1.3 and 1.4. Using Richardson's extrapolation to improve the approximation value of y(1), we obtain: 0.75 1.5 1.4333 0.5
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