's Method is a method for numeric
ally approximating value
s of a function
, given its derivative
(dy/dx) and a point
(x, y) to begin with. It is especially useful when the derivative expression
contains y's that may be otherwise difficult to resolve with integration
Begin by choosing dx; the smaller the dx, the more accurate the result, but the more numerous the steps. The initial x and y are the coordinates of the given point.
At each step, calculate dy/dx with the current x and y, multiply by dx, and add this to the current y to find the next y-value; the next x-value is the current x plus dx. Iterate as often as necessary until you reach the x for which you wish to calculate the y-value.