midtermsolutions

# midtermsolutions - MATH 480 Numerical Solution of...

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-) yGi = ,t -* f {r)= zr /4,}hJ *u**4*bİu MATH 480 Numerical Solution of Differential Equations MIDTERM EXAM April, 27st, 2011 1. (10 poinis) Given ıhat rı is a positiı'e real number. consider the jinear two-step method x. h " J-Af . .*f ) 'n_2 - QIn : 1U"-z * 4İ,-ı - İ") Determine the set of all cu such that, the mebhod. is zero-stable. Find a such that the order of accuracy is as high as possible; is the method convergent for this value of cv? T(r)= L'f . Ln *1- 'ö33 i{ für} " +aüiŞİeı {i" r9ş.: roı,dİ*İ**; İ,*, ffl]lİ f-o_-, F} ı= Ş6' =; i'6İ<4 1= bİ{f fi a 1*(1 ı bİnıls. İr'b_ i.*İ€ Fi€J Ax*\$j p \x+i? "G--?h,}_ ac E,+,_ 4z'c+-zıi - ği,r',+.ı) -{ a't+ı '2, /-'ı'A ] fay|o, eİğ&İçaş*; z4*ı,i _ 7{ğü**İtş; * ea.ee?ş: - s 3"'ü6ü +{ı!l"cİ+ \$-{İı n ÜüA6} 7 ({+h) = z{*} + hİttı -+ i* . I i' r*ı * ğ İ"ır, * s e'n'in; * Ş{ıE i /t+ızıü= z7t} *İ*ha'ü{i ., İh?etçJ r {J"'ftı*ino*"i*; _,#{*Ç it+*ü = /&} *}rv'((t ,h| ?''"i*) *{;ı* *İJ*tu} +,}/ğçj / U. -r / ' ,*42u.]+ht"-\-+"ttJut u fLr-?-f'].r*;., fi'.:i\)i'r'.hlt +7.;':' ' thzC*) = [-. ;i

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## This note was uploaded on 11/14/2011 for the course MATH 480 taught by Professor Sd during the Spring '11 term at Middle East Technical University.

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midtermsolutions - MATH 480 Numerical Solution of...

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