FORMULAS APPROXIMATING DERIVATIVES OF A FUNCTION f(x)

Fisrt Forward-Differentiation Formulas:

Fisrt Central-Differentiation Formulas:

Fisrt Backward-Differentiation Formulas:

Second Forward-Differentiation Formulas:

Second Central-Differentiation Formulas:

Second Backward-Differentiation Formulas:

 

Euler's Method: xk+1 = xk+h

yk+1 = yk+hf(xk , yk) for k=0,1,2,3,..

Heun's Method: xk+1 = xk+h

for k=0,1,2,3,..

Backward Euler's Method: xk+1 = xk+h

yk+1 = yk+hf(xk+1 , yk+1) for k=0,1,2,3,..

Fourth-Order Runge-Kutta Method:

, ,

,

Shooting Method:

Third guess =

first guess+(second guess-first guess) / (result of second guess-result of first guess)* (true value -result of first guess)