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Find the order of the one-step method h h h Un+1 = Un + „f(un +5f(un)) + (f(Un) + f(un + hf(un))) 2 21 Show that the method is at least second order. Is the method third order? How many f-evaluations does the method need per step?

Find the order of the one-step method h h h Un+1 = Un + „f(un +5f(un)) + (f(Un) + f(un + hf(un))) 2 21 Show that the method is at least second order. Is the method third order? How many f-evaluations does the method need per step?

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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1. Find the order of the one-step method Un+1 = Un + „f(un +5f(un)) + (f(Un) + f(un + hf (Un))) 4 (i) Show that the method is at least second order. (ii) Is the method third order? (iii) How many f-evaluations does the method need per step?
Transcribed Image Text:1. Find the order of the one-step method Un+1 = Un + „f(un +5f(un)) + (f(Un) + f(un + hf (Un))) 4 (i) Show that the method is at least second order. (ii) Is the method third order? (iii) How many f-evaluations does the method need per step?
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