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3. Use Taylor series expansions to determine the error in the approxima- u(t+3h)--3u(t+2h)+3u(t+h)-u(t) tion u"(t) z "' (34)Y ック 24 -3 uk+26) =u+2hu' +(262 u" t ea 24 3 u (fth) =uthul aţ u" +e 32 イy 36 q u" (6) + 1um = 24 = u"H) %3D

3. Use Taylor series expansions to determine the error in the approxima- u(t+3h)--3u(t+2h)+3u(t+h)-u(t) tion u"(t) z "' (34)Y ック 24 -3 uk+26) =u+2hu' +(262 u" t ea 24 3 u (fth) =uthul aţ u" +e 32 イy 36 q u" (6) + 1um = 24 = u"H) %3D

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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3. Use Taylor series expansions to determine the error in the approxima- tion u"(t) z u(t+3h)-3u(t+2h)+3u(t+h)-u(t) =u+3hu'+(36)e u!l+ (34 "' (34)* -3 u&+26) =u+2hu' + 24 u fthl =uthul to 24 3 l a? u" + + 13 (6) + 4" (36) num = 24 %3D 4 Find AR which make the approimation
Transcribed Image Text:3. Use Taylor series expansions to determine the error in the approxima- tion u"(t) z u(t+3h)-3u(t+2h)+3u(t+h)-u(t) =u+3hu'+(36)e u!l+ (34 "' (34)* -3 u&+26) =u+2hu' + 24 u fthl =uthul to 24 3 l a? u" + + 13 (6) + 4" (36) num = 24 %3D 4 Find AR which make the approimation
Expert Solution
Step 1

The Taylor's thoerem can be used to calculate the expansion of a function. The formula for the Taylor's series is f(x-a)=f(a)+f'(a)1!(x-a)1+f''(a)2!(x-a)2+f'''(a)3!(x-a)3+f4(a)4!(x-a)4+… .

Calculate the expansion of the function for each term in the formula. Obtain the remaining terms to determine the error.

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