What is partial differential equation? Give one example.
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Partial differential equation
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A visualisation of a solution to the two-dimensional heat equation with temperature represented by the third dimension
In mathematics, a partial differential equation(PDE) is a differential equation that contains beforehand unknown multivariable functionsand their partial derivatives. PDEs are used to formulate problems involving functions of several variables, and are either solved by hand, or used to create a computer model. A special case is ordinary differential equations(ODEs), which deal with functions of a single variable and their derivatives.
PDEs can be used to describe a wide variety of phenomena such as sound, heat, diffusion, electrostatics, electrodynamics, fluid dynamics, elasticity, or quantum mechanics. These seemingly distinct physical phenomena can be formalised similarly in terms of PDEs. Just as ordinary differential equations often model one-dimensional dynamical systems, partial differential equations often model multidimensional systems. PDEs find their generalisation in stochastic partial differential equations.
Introduction
Existence and uniqueness
Notation
Classification
Analytical solutions
Numerical solutions
See also
Notes
References
Further reading
External links
Last edited 8 days ago by an anonymous user
RELATED ARTICLES
Hyperbolic partial differential equation
partial differential equation (PDE) of order n that has a well-posed initial value problem for the first n−1 derivatives
Parabolic partial differential equation
Class of second-order linear partial differential equations
Partial differential algebraic equation

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Search
Partial differential equation
Read in another language
Watch this page
Edit

A visualisation of a solution to the two-dimensional heat equation with temperature represented by the third dimension
In mathematics, a partial differential equation(PDE) is a differential equation that contains beforehand unknown multivariable functionsand their partial derivatives. PDEs are used to formulate problems involving functions of several variables, and are either solved by hand, or used to create a computer model. A special case is ordinary differential equations(ODEs), which deal with functions of a single variable and their derivatives.
PDEs can be used to describe a wide variety of phenomena such as sound, heat, diffusion, electrostatics, electrodynamics, fluid dynamics, elasticity, or quantum mechanics. These seemingly distinct physical phenomena can be formalised similarly in terms of PDEs. Just as ordinary differential equations often model one-dimensional dynamical systems, partial differential equations often model multidimensional systems. PDEs find their generalisation in stochastic partial differential equations.
Introduction
Existence and uniqueness
Notation
Classification
Analytical solutions
Numerical solutions
See also
Notes
References
Further reading
External links
Last edited 8 days ago by an anonymous user
RELATED ARTICLES
Hyperbolic partial differential equation
partial differential equation (PDE) of order n that has a well-posed initial value problem for the first n−1 derivatives
Parabolic partial differential equation
Class of second-order linear partial differential equations
Partial differential algebraic equation

Content is available under CC BY-SA 3.0 unless otherwise noted.
Terms of Use
Privacy
Desktop
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