Numerical Methods at work

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Ordinary Differential Equations

In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, and the differential equation defines a relationship between the two. Because such relations are extremely common, differential equations play a prominent role in many disciplines including engineering, physics, economics, and biology. The below applications offer several different numerical solutions to the problem. The following methods are supported:

  • Euler
  • Runge-Kutta's 2nd, 3rd and 4th order
  • Heun-Euler
  • Bogacki-Shampine
  • Cash-Karp
  • Dormand-Prince
Euler 1707-1783
Ordinary Differential Equation vs. 1.3


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Explicit Methods

Embedded Methods




  • Graphing
  • Help
  • Method Used

Help

Explanation: Enter the ordinary differential equation that needs to be solved in the field y'=f(x,y). The usual math function can be used: +.-.*,/,(,), abs(), acos(), asin(), atan(), atan2(), cos(), exp(), log(), pow(), sin(), sqrt(), tan(). Note for something like y^3 used the pow(y,3) notation.
Type in the interval range in x= and set the initial conditions in Initial y(x0). Finally, select how many intervals that should be subdivided in the x interval specified. Select one or more methods you like to use or compare to solving the ordinary differential. Checkmark the Verbose printout details for each interval step.

The tab (Graphing) graphs the equations in the interval given. The Test button set up a default differential (for testing only).
Email: hve@hvks.com if you have any questions.
This version has been tested with both Edge, Chrome, Firefox & Safari browsers.

Method used

The different methods are implemented using a Butchers tableau for each method.
For more information see Numerical_ordinary_differential_equations

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Corrections:
21-Nov-2023vs 1.3Switch to the Plotly library
10-Nov-2019vs 1.2Redesign GUI
2011-Nov-25vs 1.1Initial release