Lecture 41

# Lecture 41 - System of ODEs A system of simultaneous ODEs n...

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System of ODEs A system of simultaneous ODEs n equations with n initial conditions = = = ) , , , , ( ) , , , , ( ) , , , , ( n 2 1 n n n 2 1 2 2 n 2 1 1 1 y y y t f dt dy y y y t f dt dy y y y t f dt dy

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System of ODEs Bungee Jumper’s velocity and position Two simultaneous ODEs 2 (0) (0) 0 d c g v m dx v dt dv dt x v = = - = = = = t m gc c m t x t m gc c gm t v d d d d cosh ln ) ( tanh ) ( 2 2 d x dt = 0 t dx dt = =
A second-order ODE can be converted to a SYSTEM of 2 ODEs Convert to two first-order ODEs = = = 1 0 0 0 2 2 ) (t dt dy t y dt dy y t g dt y d α , ) ( ) , , ( = = = = = = = = 1 0 2 0 0 1 2 1 2 2 2 2 1 2 1 t y t y s C I y y t g dt y d dt dy y dt dy dt dy dt dy y y y let ) ( ) ( . . ) , , (

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Euler’s Method Any method considered earlier can be used Euler’s method for two ODE-IVPs Basic Euler method Two ODE-IVPs y y t hf y y
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Lecture 41 - System of ODEs A system of simultaneous ODEs n...

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