Maple Working Rules for Newton-Raphson Method

 Newton-Raphson Method


The Newton-Raphson method is based on the principle that if the initial guess of the root of f(x)=0 is at x(i), then if one draws the tangent to the curve at f(x(i)), the point x(i+1) where the tangent crosses the -axis is an improved estimate of the root (Figure 1).

Using the definition of the slope of a function, at x=x(i) 

Equation (1) is called the Newton-Raphson formula for solving nonlinear equations of the form f(x)=0.  So starting with an initial guess, x(i), one can find the next guess, x(i+1), by using Equation (1).  One can repeat this process until one finds the root within a desirable tolerance.


Maple Setup

[> NewtonsMethod(x^3 + 4*x - 10, x = 1);

                          1.556773264


[> NewtonsMethod(x^3 + 4*x - 10, x = 2, output = sequence);

2, 1.625000000, 1.558650066, 1.556774723, 1.556773264, 1.556773264


[> NewtonsMethod(x^3 + 4*x - 10, x = 0, view = [0 .. 3, DEFAULT], output = animation);




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