Taylor Series Expansion

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Taylor Series Method The problem to be solved is a first order ODE: dy( x) dx f ( x , y ), y ( x 0 ) y 0 Estimates of the solution at different base points: y ( 0 x0 h), y( x0 2h), y( x 3h), .... are computed using the truncated Taylor series expansions. 18
Taylor Series Expansion Truncated Taylor Series Expansion y( x 0 h) n k h k! k d y dx k k 0 xx , y y 0 0 y( x 0 ) h dy dx xx y y 0 0 , 2 h 2! 2 d y 2 dx xx y y 0 0 , ... n h n! n d y n dx xx y y 0 0 , The n th order Taylor series method uses the n th order Truncated Taylor series expansion. 19
Page 1 and 2: The If the Taylor Series Expansion
Page 3 and 4: What If we change the interval ? If
Page 5 and 6: Finite Differences for Derivation T
Page 7 and 8: Example : Derivation of Forward Dif
Page 9 and 10: Example : Derivation of Forward Dif
Page 11 and 12: Derivatives of Bivariate & Multivar
Page 13 and 14: Second Partial Derivatives hk k y h
Page 15: Second Partial Derivatives Followin
Page 20 and 21: Euler Method • First order Taylor
Page 22 and 23: 22 Euler Method 1,2,... ) , ( ) ( M
Page 24 and 25: Interpretation of Euler Method y 1
Page 26 and 27: Example 1 Use Euler method to solve
Page 28 and 29: Example 1 f 2 ( x, y) 1 x , x0 1, y
Page 30 and 31: Example 1 f 2 ( x, y) 1 x , x0 1, y
Page 32 and 33: Second Order Taylor Series Methods
Page 34 and 35: 34 High Order Taylor Series Methods
Page 36 and 37: Example 2 Second order Taylor Serie
Page 38 and 39: 38 Example 2 )) 2 (1 4 1 ( 2 ) 2 (1
Page 40 and 41: Programming Euler Method Write a MA
Page 42 and 43: Programming Euler Method f=inline('
Page 44 and 45: Example 1: Find y(0.5) if y is the
Page 46 and 47: Example 3: Solve the differential e
Page 48: Comparison of numerical and analyti

Taylor Series Expansion

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