Talk:Partial differential equation

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Rewrite needed

Can somebody who understands this article rewrite the following please? "Partial differential equations also occupy a large sector of pure mathematical research, in which the usual questions are, broadly speaking, on the identification of general qualitative features of solutions of various partial differential equations, such as existence, uniqueness, regularity, and stability." As is, it is incomprehensible. Perhaps break it into two or three sentences? — Preceding unsigned comment added by 2600:1702:170:3B90:252F:91F:542:7612 (talk) 17:59, 26 October 2022 (UTC)

I agree that area is incomprehensible. I find the entire article to be incomprehensible. Start over. Boil it down to exactly what is a PDE. Precisely. Explain each part precisely. Only then go into why PDE's are useful, and solutions and etc..

J Mark Morris (talk) 01:44, 20 May 2024 (UTC)

Even the first sentence is very confusing: "In mathematics, a partial differential equation (PDE) is an equation which computes a function between various partial derivatives of a multivariable function." I cannot tell what the word "between" is supposed to mean there, and an equation doesn't "compute" anything. 74.96.10.88 (talk) 15:01, 10 December 2024 (UTC)

Conceptual Definition

Arnold defines an ODE in his book as a system evolving in time having the following properties: (1) determinancy (2) finite dimensionality (3) smoothness

where by determinancy he means that the initial data of the problem completely specifies the future and the past of the system. By a finite dim. system he means one whose phase space can be localy parametrized by finite many real numbers. The smoothness property means that the system has a smooth phase space (ie. the phase space is a differentiable manifold, eg. The plane, the real line) and smooth evolution function.

What i would like to know is if there exists such a nice conceptual definition of a PDE.

Wiki Education assignment: 4A Wikipedia assignment

— Assignment last updated by Lzepeda12 (talk) 21:08, 26 April 2023 (UTC)

Comparison with simple differential equations

It would be nice to have an explanation of the difference between simple differential equations in one variable and partial differential equations in multiple variables, with worked examples. The current article tells us how they are used but not the very basic step of what happens to the other variables, an explanation of which would let people take the step between the two more easily. Robin Murison (talk) 10:58, 20 April 2023 (UTC)

"Numerical solutions of partial differential equations" listed at Redirects for discussion

File:Information.svg The redirect Numerical solutions of partial differential equations has been listed at redirects for discussion to determine whether its use and function meets the redirect guidelines. Readers of this page are welcome to comment on this redirect at Template:Section link until a consensus is reached. 1234qwer1234qwer4 17:34, 12 June 2025 (UTC)