Client Account:   Login
Home Site Statistics   Contact   About Us   Sunday, February 25, 2018

users on-line: 2 | Forum entries: 6   
Pj0182295- Back to Home
   Skip Navigation LinksHOME › AREAS OF EXPERTISE › Differential Equations Methods

OVERVIEW
Ordinary Differential Equations

Several numerical methods can be used to solve ordinary differential equations. These equations are especially useful when differential equations cannot be solved analytically.

The general form of the first-order equations can be expressed by:

y' = f (x,y)

and the higher-order equations can be written:

y(n) = f (x, y, y', y'',..., y(n-1))

The task is to determine the necessary boundary conditions and the relationships between x and y.

A common way of handling a second- or higher-order equations is to replace it with an equivalent system of first-order equations. The higher-order equation above can always be transformed into a set of n first order equations. Using the notation:

y0 = y
y1 = y'
y2 = y''
·
·
·
y(n-1) = y(n-1)

then the equivalent first-order equations become:

y'0 = y1
y'1 = y2
y'2 = y3
·
·
·
y'n = f ( x, y0, y1,..., yn-1)





Skip Navigation Links.

Home

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

EIGENVALUE SOLUTIONS...
  Eigen Inverse Iteration
  Rayleigh-Quotient Method

INTERPOLATION APPLICATIONS...
  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...

Differentiation
     Home Intergration
Consider the function where...

Integration
 

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