Ode and pde-the major difference

In summary, the conversation discusses various numerical methods that are used to solve differential equations. These methods include Finite Element Method, Boundary Element Method, Finite Differences Method, and Finite Volume Method. These methods are not required, but can be helpful in solving differential equations. The conversation also distinguishes between Ordinary Differential Equations and Partial Differential Equations, which involve solutions of functions of single and multiple variables, respectively.
  • #1
chandran
139
1
i will express some function y as follows as its ordinary derivative

dy/dt=y

(can i say like this-the change in y value with respect to change in t value at the point t will be equal to the y value at t)

Can somebody explain a partial derivative like the above statement

What is so special in a partial differential equation that it requires so many methods as follows. What is the difficulty that makes the ode and pde different in their solution

1)fem
2)bem
3)fdm
4)fvm
 
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  • #2
don't mind but what do u'r short forms , viz
1)fem
2)bem
3)fdm
4)fvm
mean?
 
  • #3
I would hazard:
1) Finite element method
2) ?
3) Finite differences method
4) Finite volume method

These are all NUMERICAL methods, none of them are "required", but options that have shown themselves handy in solving diff.eqs.
 
  • #4
Ordinary Differential Equations are equations that involve solutions of functions of single variables.

Therefore, f(x) etc...

Partial Differential Equations are equations that involve solutions of functions of multiple variables.

So for instance f(x,y)
 
  • #5
bem: bug eyed monster? I.e. appealing to an alien race to solve your equations for you!
 
  • #7
Is that the same as the common Boundary Value Problem...

<should've looked at link first...>

<looks>

no! :)
 

1. What is the difference between ODE and PDE?

ODE stands for Ordinary Differential Equation, while PDE stands for Partial Differential Equation. The main difference between the two is that ODEs involve only one independent variable, while PDEs involve multiple independent variables.

2. How are ODEs and PDEs used in science?

ODEs and PDEs are used to mathematically model various physical phenomena in science, such as heat transfer, fluid dynamics, and population growth. They allow scientists to make predictions and understand complex systems.

3. What are some common examples of ODEs and PDEs?

Some common examples of ODEs include the simple harmonic oscillator, radioactive decay, and population growth models. PDEs are often used to describe wave phenomena, such as the heat equation and the Schrödinger equation.

4. How do you solve ODEs and PDEs?

ODEs and PDEs can be solved using various analytical and numerical methods. Analytical methods involve finding exact solutions to the equations, while numerical methods involve approximating solutions using computer algorithms.

5. What are the applications of solving ODEs and PDEs?

Solving ODEs and PDEs has many practical applications, such as predicting the behavior of electrical circuits, designing structures for optimal heat transfer, and understanding the spread of diseases. They are also used in fields like engineering, physics, and economics.

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