Ode, pde, dde, sde, dae ?

  • Thread starter Elwin.Martin
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In summary, an ODE (ordinary differential equation) involves a single independent variable and its derivatives, while a PDE (partial differential equation) involves multiple independent variables and their partial derivatives. DDEs (delay differential equations) are commonly used to model systems with time delays, such as population dynamics, chemical reactions, and neural networks. In finance, SDEs (stochastic differential equations) are used to model the unpredictable behavior of stock prices and other financial instruments, and to calculate the probability of certain outcomes. DAEs (differential-algebraic equations) involve both derivatives and algebraic equations, and are commonly used to model systems with constraints. Numerical methods can be used to solve both ODEs and PDEs
  • #1
Elwin.Martin
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Okay, kind of a silly question...but what do all of these stand for?

ODE=Ordinary Differential Equations ( ;O I hope this is right, I took a course on this stuff)

PDE=Partial Differential Equations ( Hope this is right too, taking this next semster)

DDE=...?

SDE=...?

DAE=...?

Thank you in advanced!
 
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  • #3
Only the five? Or we have more categories of these DEs?
 
  • #4
DDE= Delay differential equations

SDE= Stochastic differential equations

DAE= Differential algebraic equations
 
  • #5


No problem, happy to help clarify! DDE stands for Delay Differential Equations, which involve equations where the derivative depends on the function evaluated at a previous time. SDE stands for Stochastic Differential Equations, which involve randomness or uncertainty in the equations. DAE stands for Differential-Algebraic Equations, which involve a combination of differential and algebraic equations. These types of equations are commonly used in various fields of science and engineering to model and understand complex systems. I'm glad to hear you are interested in learning more about them!
 

1. What is the difference between an ODE and a PDE?

An ODE (ordinary differential equation) involves a single independent variable and its derivatives, while a PDE (partial differential equation) involves multiple independent variables and their partial derivatives.

2. What are some real-world applications of DDEs?

DDEs (delay differential equations) are commonly used to model systems with time delays, such as population dynamics, chemical reactions, and neural networks.

3. What is the importance of SDEs in finance?

SDEs (stochastic differential equations) are used in finance to model the unpredictable behavior of stock prices and other financial instruments. They also provide a way to calculate the probability of certain outcomes in these systems.

4. How do DAEs differ from ODEs and PDEs?

DAEs (differential-algebraic equations) involve not only derivatives, but also algebraic equations, making them more complicated to solve than ODEs and PDEs. They are commonly used to model systems with constraints and are often solved numerically.

5. Can numerical methods be used to solve ODEs and PDEs?

Yes, numerical methods such as Euler's method, the Runge-Kutta method, and finite difference methods can be used to approximate solutions to both ODEs and PDEs. These methods are particularly useful for complex systems where analytical solutions are not possible.

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