where
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Numerical solution of differential equations
Taylor's method
To solve dy/dx = f(x,y) , subject to y(x0) = y0
where
x1 = x0 + h and
y1 = y(x1)
y'0 stands for y'(x0)
Euler's method
To solve dy/dx = f(x,y) , subject to y(x0) = y0
yn+1 = yn + h f ( xn , yn ) , n = 0,1,2, ...
where
xn+1 = xn + h and
yn = y(xn)
yn+1 = y(xn+1)
Runge- Kutta Method
To solve dy/dx = f(x,y) , subject to y(x0) = y0
where
x1 = x0 + h and
y1 = y(x1)
Milne's predictor corrector method
To solve dy/dx = f(x,y) , subject to
y(x0) = y0 , y(x1) =y1 , y(x2) =y2 , y(x3) =y3
where x0 , x1 , x2 , x3 are equally spaced.
predictor formula is
corrector formula is
where
x4 = x3 + h and
y4 = y(x4)
y'i stands for y'(xi)
Adam bashforth's predictor corrector method
To solve dy/dx = f(x,y) , subject to
y(x0) = y0 , y(x1) =y1 , y(x2) =y2 , y(x3) =y3
where x0 , x1 , x2 , x3 are equally spaced.
predictor formula is
corrector formula is
where
x4 = x3 + h and
y4 = y(x4)
y'i stands for y'(xi)
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