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What is a Delay Differential Equation?

A Delay Differential Equation (or DDE) is a differential equation in which the derivative of the function in one instant of time depends on the value of the function in previous instants. In mathematical terms,

where .

 

EJS can only solve DDEs with delays that are both discrete and constant. That is, equations of the form:

where   remain constant while the DDE is being solved. (Though they can change value if the DDE is conveniently reinitialized. That is, you can associate the delays with a variable, but you need to reset the solver if you change the value of this variable.)

 

So, for instance, EJS:

  • CAN solve the following DDEs:

 

  • but CANNOT solve the DDE:
    • (Pantograph’s equation)

 

But, if EJS can solve your DDE, then you can expect all the goodies you are familiar with for ODEs:

  • a good variety of algorithms available
  • fine control on the algorithm’s parameters
  • possibility to write preliminary code
  • event handling
  • error handling



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Page last modified on March 26, 2011, at 08:09 PM