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Unformatted text preview: Lecture 2  EE743 Lecture 2  EE743 Numerical Solution of Differential Equations Professor: Ali Keyhani Professor: Ali Keyhani 2 Numerical Solution of Differential Equations Eulers Method 3 Approximation by the Eulers Method = = = t t dt t x f t x t x f t x dt dx ) , ( ) ( ) , ( ) ( + + + = = t t n A A A dt t x f t x 2 1 ) , ( ) ( Numerical Solution of Differential Equations 4 Numerical Solution of Differential Equations ( 29 ( 29 ( 29 ( 29 [ ] ( 29 1 1 1 2 1 ) ( ) ( ) ( ) ( ) ( t x t A t x f t x t x t t x t x t t x t t x t t x t x t t t t t = = + = = +  + = = = = 5 Numerical Solution of Differential Equations ( 29 [ ] n n n n t t x f t t x t x , ) ( ) ( 1 1 + + + = ( 29 ( 29 ( 29 ( 29 [ ] 1 1 2 1 1 2 1 2 ) ( ) ( ) ( ) ( ) 2 ( t x f t t x t A t x t t x t x t t x t t x t x t t x = = + = + + = = + 6 Trapezoidal Integration Method Numerical Solution of Differential Equations 7 Numerical Solution of Differential Equations ( 29 ( 29 ( 29 ( 29 ) ( ) ( ) ( ) ( 2 ) ( ) ( 2 ) ( ) ( 2 1 2 ) , ( ) ( ) , ( 1 1 1 1 1 1 1 1 1 3 2 1 t x f t x t x f t x t x t x t A t x f t x f t A x x t A j for x x t A A A A A A dt t x f t x t x f x dt dx o o j j j j j t t n j = = + = +...
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 Spring '08
 Keyhani

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