utf-8''Chap2 Lec3 Euler Methhod (Student)

utf-8''Chap2 Lec3 Euler Methhod (Student) - H UT –...

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Unformatted text preview: H UT – DEPARTM ENT OF M ATH . APPLI ED ---------------------------------------------------------------------------------------------------------- I DE – ADVANCED PROGRAM CH APTER 2: M athematical M odels and Numer ical M ethods (1 weeks) • LEC 3: EULER’S M ETH OD (FOR STUDENT) • PhD. N GUYEÃN QUOÁC LAÂN (9/2007) CONTENTS------------------------------------------------------------------------------------------------------------------------------- 3.3 M athematical model: Radioactive decay 3.1 Euler ’s M ethod 3.2 Example I DEA---------------------------------------------------------------------------------------------------------------------------------------- Answe r : a/ The pr oblem is non – linear → Gener ally, we can’t solve it! The initial value (Cauchy’s) pr oblem: a/ The pr oblem is linear or non – linear ? Can you solve it? - = ≥ +- = 2 ) ( , 2 ' 2 y x e y y y x b/ Appr oximate its solution at x = 0.5, x = 1 with step h = 0.5 b/ To appr oximate its solution: We must appr oximate y’(x ): ( 29 ( 29 ( 29 h x y h x y x y '- + ≈ ( 29 ( 29 ( 29 ( 29 2 2 e x y x y h x y h x y ⋅ +- =- + ⇒ = x 5 . 1 = = + x h x 1 2 1 = = + x h x TH E NUM ERI CAL SOLUTI ON----------------------------------------------------------------------------------------------------------------------------------------...
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This note was uploaded on 11/02/2009 for the course ECE ece464 taught by Professor Abc during the Spring '09 term at Jacksonville College.

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utf-8''Chap2 Lec3 Euler Methhod (Student) - H UT –...

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