Home Site Statistics   Contact   About Us   Thursday, July 19, 2018

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

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)

Please select from the menu  →         PRESS TO SELECT      

You are viewing this tab ↓
Skip Navigation Links.


Home Math, Analysis & More,
  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 Integration
Consider the function where...

  KMP Engineering  
 Location: 2461 E Orangethorpe Ave. 
 Fullerton, CA 92631 USA Email:info@keystoneminingpost.com

2006-2018 All rights reserved© KMP Engineering