Solving a Partial Differential Equation (PDE)

Thread starter kirppu
Start date May 16, 2012
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Differential Differential equation Partial Pde

In summary, a Partial Differential Equation (PDE) is a mathematical equation that involves an unknown function of multiple variables and its partial derivatives. It is commonly used to describe physical phenomena such as heat transfer, fluid dynamics, and quantum mechanics. The main difference between a PDE and an Ordinary Differential Equation (ODE) is that a PDE involves partial derivatives, while an ODE involves only ordinary derivatives. The process of solving a PDE involves finding a function that satisfies the equation and any given boundary or initial conditions, which can be done analytically or numerically. PDEs have a wide range of applications in various fields of science and engineering, including economics, finance, and image processing. There are also various software tools available for

May 16, 2012

kirppu

Hi,

Can somebody help me solve the following PDE?

∂p(x,t)/∂t = -p(x,t) + ∫λ(x-x')p(x',t)dx'

with p(x,0)=δ(x)

Thanks a lot

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May 16, 2012

kirppu

It corresponds to the Kolmogorov-Feller equation.

May 17, 2012

hunt_mat

Homework Helper

Have you thought about taking Laplace transforms?

1. What is a Partial Differential Equation (PDE)?

A Partial Differential Equation (PDE) is a mathematical equation that involves an unknown function of multiple variables and its partial derivatives. It is commonly used to describe physical phenomena such as heat transfer, fluid dynamics, and quantum mechanics.

2. What is the difference between a PDE and an Ordinary Differential Equation (ODE)?

The main difference between a PDE and an ODE is that a PDE involves partial derivatives, while an ODE involves only ordinary derivatives. This means that a PDE describes a system that varies in more than one independent variable, while an ODE describes a system that varies in only one independent variable.

3. How do you solve a PDE?

The process of solving a PDE involves finding a function that satisfies the equation and any given boundary or initial conditions. This can be done analytically, using mathematical techniques such as separation of variables or the method of characteristics, or numerically using computer algorithms.

4. What are the applications of PDEs?

PDEs have a wide range of applications in various fields of science and engineering. They are commonly used to model physical phenomena such as heat transfer, fluid dynamics, and electromagnetism. PDEs are also used in economics, finance, and image processing.

5. Are there any software tools available for solving PDEs?

Yes, there are various software tools available for solving PDEs. These include commercial software such as MATLAB and Mathematica, as well as open-source software such as FreeFem++ and FEniCS. These tools use numerical methods to solve PDEs and can handle complex and high-dimensional problems.