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'''NewtonRaphson.bas

''19/11/2002

''Version 1.0

''By Adolfo Leon Sepulveda

''Get a function''s root by Newton-Raphson Method

''example:

'' Function: f(x)= x^2 - 4

'' Input:

'' x0 : 4

'' Result:

'' Raiz = 2

Declare func f(x)

Declare func fdx(x,dx)

Declare func NewtonRaphson(x0,h,iter, byref status)

const dx=1.0e-6

const iter=100

status = 0

input "x0: ",x0

raiz = NewtonRaphson(x0,dx,iter, status)

if status then

print "Raiz = ";raiz

else

print "function No converge"

endif

end

func NewtonRaphson(x0,dx,iter, byref status)

local i,x

print " x f(x) f''(x)"

i=1

repeat

x = x0 - f(x0) / fdx(x0,dx)

error = abs((x-x0)/x0)

print using "###0.0000 ###0.0000 ###0.0000" ;x0,f(x0),fdx(x0,dx)

if error < dx then exit loop

x0 = x

i=i+1

until i > iter

if i > iter then

status = 0

NewtonRaphson = 0

else

status = 1

NewtonRaphson = x

endif

end

func f(x)

f= x^2-4.0

end

func fdx(x,dx)

local a,b,c,d

''Richardson''s extrapolation for first derived

''-1 / (6*h) * (f(x+h) - 8*f(x + h/2) - f(x-h) + 8*f(x-h/2))

a = f(x+dx)

b = f(x + dx/2.0)

c = f(x-dx)

d = f(x-dx/2.0)

fdx = -1.0 / (6.0*dx) * (a - 8.0*b - c + 8.0*d)

end

smallbasic.github.io/samples/node/118.bas at master · smallbasic/smallbasic.github.io · GitHub

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