Beta
ManageSearchChatDiscover
243392

Review on the applications of 2nd order linear P.D.E

Article

Last updated: 04 Jan 2025

OverviewSimilar Items

Subjects

-

Tags

-

Abstract

PDEs are very important in dynamics, elasticity, heat transfer, electromagnetic theory, and quantum mechanics by adding a few statistics to PDE it can be used in weather forecasting, prediction of crime places, disasters, how universe behave ……. Etc.
second order linear PDEs can be classified according to the characteristic equation into 3 types hyperbolic, parabolic and elliptic.
Hyperbolic equations have two distinct families of (real) characteristic curves, parabolic equations have a single family of characteristic curves, and the elliptic equations have none. All the three types of equations can be reduced to its first canonical form finding the general solution or the second canonical form similar to 3 basic PDE models.
Hyperbolic equations reduce to a form coinciding with the wave equation in the leading terms, the parabolic equations reduce to a form modeled by the heat equation, and the Laplace's equation models the canonical form of elliptic equations. Thus, the wave, heat and Laplace's equations serve as basic canonical models for all second order linear PDEs.

DOI

10.21608/iugrc.2021.243392

Keywords

Partial differential equation, parabolic equation, hyperbolic equation, elliptical equation, canonical form

Authors

First Name

Ahmed

Last Name

farg

MiddleName

Saeed

Affiliation

New Cairo academy, 5th settlement, Egypt.

Email

ahmedgomea81@yahoo.com

City

-

Orcid

-

First Name

A.

Last Name

Abd Elbary

MiddleName

M.

Affiliation

Department of Mathematics and Physical Science, New Cairo Academy, Higher Institute of Engineering and Technology, New Cairo City, Egypt.

Email

dr_ah_abdelbary2005@yahoo.com

City

-

Orcid

-

Volume

5

Article Issue

5

Related Issue

34928

Issue Date

2021-08-01

Receive Date

2022-06-12

Publish Date

2021-08-01

Page Start

9

Page End

17

Article File

IUGRC_Volume 5_Issue 5_Pages 9-17.pdf

PDF . 1.9MB

Link

https://iugrc.journals.ekb.eg/article_243392.html

Detail API

https://iugrc.journals.ekb.eg/service?article_code=243392

Order

2

Type

Original Article

Type Code

762

Publication Type

Journal

Publication Title

The International Undergraduate Research Conference

Publication Link

https://iugrc.journals.ekb.eg/

MainTitle

Review on the applications of 2nd order linear P.D.E

Details

Type

Article

Created At

22 Jan 2023