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6. (a) Show that the explicit trapezoidal method for y'= f(y) is second order accurate. (b) Show that the explicit midpoint method for y'= f(y) is second order accurate. [Hint: You need to compare derivatives of y with their expressions in terms of f and show that terms that are not (h²) cancel in the expression for d,. Use the identities y'= f and y"=y=fyf.)

6. (a) Show that the explicit trapezoidal method for y'= f(y) is second order accurate. (b) Show that the explicit midpoint method for y'= f(y) is second order accurate. [Hint: You need to compare derivatives of y with their expressions in terms of f and show that terms that are not (h²) cancel in the expression for d,. Use the identities y'= f and y"=y=fyf.)

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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6. (a) Show that the explicit trapezoidal method for y'= f(y) is second order accurate. (b) Show that the explicit midpoint method for y'= f(y) is second order accurate. [Hint: You need to compare derivatives of y with their expressions in terms of f and show that terms that are not (h²) cancel in the expression for d,. Use the identities y' = f and y"=y=fyf.)
Transcribed Image Text:6. (a) Show that the explicit trapezoidal method for y'= f(y) is second order accurate. (b) Show that the explicit midpoint method for y'= f(y) is second order accurate. [Hint: You need to compare derivatives of y with their expressions in terms of f and show that terms that are not (h²) cancel in the expression for d,. Use the identities y' = f and y"=y=fyf.)
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