Receptor_Kinetics2

Receptor_Kinetics2 - L+ R K 2 K1 RL L(0) R(0) RL(0) dL(t )...

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1 2 K K L RR L ⎯⎯→ ←⎯⎯ + 12 () , (0) , , dL t KL t R t K R L t L dt dR t t R t K R L t R dt dRL t K Lt Rt K RLt RL dt =− + + =⋅
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Numerical Solution of a Single Differential Equation Problem () (( ) ,) , ( 0 ) dx t f xt t x c dt = = 22 2( ) , ( 0 ) (), (0) sin( ) ( ) , dx t xt x c dt dx t tx t x c dt dx t t x c dt =− = = = −=
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Euler’s Method • Graphical Interpretation () (( ) ,) , ( 0 ) dx t f xt t x c dt == h=0.1 h=0.2 h=0.4 (), (0) 4 dx t kx t x dt = −=
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Euler’s Method • Definition of Derivative () ( ) dx t x t h x t dt h + ( ) (( ) , ) xt h xt f xt t h + ( ) ( ( ) , ) h f xt t += + ) ,) , ( 0 ) dx t f xt t x c dt = =
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Euler’s Method • From Taylor Series Expansion () (( ) ,) , ( 0 ) dx t f xt t x c dt = = 2 1 ( ) ( ) '( ) ''( ) 2! xt h xt h x t hx t += + + + " ( ) ' ( ) +≅ +
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Example 1 () 2( ) , ( 0 ) 4 dx t xt x dt = −= ( ) ( ( ) , ) xt h h f xt t + =+ let 0 (0.1) (0) 0.1 ( (0),0) 40 . 1 ( 4 , 0 ) 4 0.1 ( 8.0) 3.2 tx x f x f x == + =
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Example 1 (continue) () 2( ) , ( 0 ) 4 dx t xt x dt = −= ( ) ( ( ) , ) xt h h f xt t + =+ let 0.1 (0.2) (0.1) 0.1 ( (0.1),0.1) 3.2 0.1 (3.2,0.1) 3.2 0.1 ( 2.0 3.2) (0.2) 2.56 tx x f x f x == + =
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Example 2 () ( ) ( ( ) , ) xt h xt h f xt t + =+ 22 () , (0) 1 dx t tx t x dt = −= let 0 (0.1) (0) 0.1 ( (0),0.0) 1.0 0.1 (1.0,0.0) 1.0 0.1 ( 0.0 1.0 ) 1.0 x f x f x == + =
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This note was uploaded on 04/09/2008 for the course BME 210 taught by Professor D'argenio during the Spring '07 term at USC.

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Receptor_Kinetics2 - L+ R K 2 K1 RL L(0) R(0) RL(0) dL(t )...

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