Client Account:   Login
Home Site Statistics   Contact   About Us   Monday, April 23, 2018

users on-line: 2 | Forum entries: 6   
j0110924 - Back to Home
   Skip Navigation LinksHOME › AREAS OF EXPERTISE › Differential Equations Methods › ~ Euler Method

      Skip Navigation Links

Euler Method

The simplest method for the numerical integration of a first-order ordinary differential equation is Euler's method. Consider the problem:

dx/dy = f (x, y) = g (x)

This method assume that for a small distance ∆x along the x-axis from some initial point x0, the function g(x) is a constant equal to g(x0).

dx/dy |x=x0 = f (x0, y0) = g(x0)

Assuming that g(x) = g(x0) for all values of x between x0 and x1 = x + ∆x, then the change in y corresponding to the small change ∆x in x is given approximately by:

∆x/∆y = f (x0, y0)

If y1 is used to denote y0 + ∆y, then the above equation becomes:

y1 = y0 + ∆x f (x0, y0) = y0 + h f (x0, y0)

where h = ∆x; y1 can then be calculated from the above equation. This completes the solution process for one step along the x-axis. The process can be repeated by using the previous solution as the starting values for the current step, yielding a general solution:

y2 = y1 + h f (x1, y1)
y2 = y2 + h f (x2, y2)
yn + 1 = yn + h f (xn, yn)

This is known as Euler's method. The calculation process, step by step, along the x-axis from the initial point x0 to the required finishing point.

One of our main algorithm implementation mechanisms include writing algorithms using differential equations. The next tab shows the solution and numerical implementation of a first-order differential equation.

Skip Navigation Links.


Home Math, Analysis & More,
  our established expertise..."

  Eigen Inverse Iteration
  Rayleigh-Quotient Method

  Cubic Spline Method
  Newton Divided Difference


Applied Mathematical Algorithms

     Home Complex Functions
A complex number z = x + iy, where...

Complex Functions
     Home Non-Linear Systems
Non-linear system methods...

Non Linear Systems
     Home Differentiation
Construction of differentiation...

     Home Intergration
Consider the function where...


2006-2018 © Keystone Mining Post  |   2461 E. Orangethorpe Av., Fullerton, CA 92631 USA  |