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1. Hyperbolic partial differential equation: In mathematics, a hyperbolic partial differential equation of order n {\displaystyle n} is a partial differential equation (PDE) that, roughly speaking, has a well-posed initial value problem for the first n − 1 {\displaystyle n-1} derivatives. More precisely, the ... (Type of partial differential equations) [100%] 2023-12-31 [Hyperbolic partial differential equations]
2. Hyperbolic partial differential equation: at a given point $ M( x _ {1} \dots x _ {n} ) $ A partial differential equation for which the Cauchy problem is uniquely solvable for initial data specified in a neighbourhood of $ M $ on any non-characteristic surface (cf. Characteristic ... (Mathematics) [100%] 2023-10-17
3. Partial differential equations: Partial differential equations (PDEs) are the most common method by which we model physical problems in engineering. Finite element methods are one of many ways of solving PDEs. [84%] 2023-12-29 [Finite element analysis] [Computational solid mechanics]...
4. Hyperbolic partial differential equation, numerical methods: Methods for solving hyperbolic partial differential equations using numerical algorithms. Various mathematical models frequently lead to hyperbolic partial differential equations. (Mathematics) [81%] 2023-08-21
5. Partial differential equation: A partial differential equation (or briefly a PDE) is a mathematical equation that involves two or more independent variables, an unknown function (dependent on those variables), and partial derivatives of the unknown function with respect to the independent variables. The ... [80%] 2021-12-24 [Dynamical Systems] [Applied Mathematics]...
6. Partial differential equation: In mathematics, a partial differential equation (PDE) is an equation which computes a function between various partial derivatives of a multivariable function. The function is often thought of as an "unknown" to be solved for, similar to how x is ... (Type of differential equation) [80%] 2023-12-30 [Partial differential equations] [Multivariable calculus]...
7. Differential equation, partial: An equation of the type $$ \tag{1 } F ( x, \dots, p _ {i _ {1} \dots i _ {n} } ,\dots ) = 0 . $$ Here $ F $ is a given real-valued function of the points $ x = ( x _ {1}, \dots, x _ {n ... (Mathematics) [80%] 2023-10-22
8. Partial differential equation: A partial differential equation, or a PDE, is an equation giving a relationship between a function of multiple variables and its derivatives. Any function satisfying this equation is known as a solution of the PDE. [80%] 2023-06-09
9. Abstract hyperbolic differential equation: Consider the Cauchy problem for the symmetric hyperbolic system (cf. also Hyperbolic partial differential equation) $$ \begin{cases} \frac { \partial u } { \partial t } + \sum _ { j = 1 } ^ { m } a _ { j } ( x ) \frac { \partial u } { \partial x _ { j } } + c ( x ... (Mathematics) [75%] 2023-10-27
10. Linear hyperbolic partial differential equation and system: A partial differential equation (or system) of the form $$ \tag{1 } \sum _ {| \alpha | \leq m } a _ \alpha ( x) D ^ \alpha u = f $$ for which at any point $ x = ( x _ {0}, \dots, x _ {n} ) $ of its domain ... (Mathematics) [75%] 2023-10-13
11. Delay partial differential equations: A delay partial differential equation (DPDE) is an equation which involves Therefore, a delay partial differential equation differs from a partial differential equation in that it depends not only on the solution at a present stage but also on the ... [72%] 2021-12-24 [Dynamical Systems] [Numerical Analysis]...
12. Numerical partial differential equations: Numerical partial differential equations is the branch of numerical analysis that studies the numerical solution of partial differential equations (PDEs). In this method, functions are represented by their values at certain grid points and derivatives are approximated through differences in ... [72%] 2023-12-30 [Numerical differential equations] [Partial differential equations]...
13. Journal of Hyperbolic Differential Equations: The Journal of Hyperbolic Differential Equations was founded in 2004 and carries papers pertaining to nonlinear hyperbolic problems and related mathematical topics, specifically on the theory and numerical analysis of hyperbolic conservation laws and of hyperbolic partial differential equations arising ... [70%] 2022-09-23 [Mathematics journals]
14. Elliptic partial differential equation: at a given point $ x $ A partial differential equation of order $ m $, $$ \sum a _ {i _ {1} \dots i _ {n} } ( x) \frac{\partial ^ {m} u }{\partial x _ {1} ^ {i _ {1} } \dots \partial x _ {r} ^ {i ... (Mathematics) [69%] 2024-01-21
15. Parabolic partial differential equation: A parabolic partial differential equation is a type of partial differential equation (PDE). Parabolic PDEs are used to describe a wide variety of time-dependent phenomena, including heat conduction, particle diffusion, and pricing of derivative investment instruments. (Class of second-order linear partial differential equations) [69%] 2023-12-29 [Parabolic partial differential equations]
16. Nonlinear partial differential equation: In mathematics and physics, a nonlinear partial differential equation is a partial differential equation with nonlinear terms. They describe many different physical systems, ranging from gravitation to fluid dynamics, and have been used in mathematics to solve problems such as ... [69%] 2023-12-29 [Partial differential equations] [Solitons]...
17. Separable partial differential equation: A separable partial differential equation is one that can be broken into a set of separate equations of lower dimensionality (fewer independent variables) by a method of separation of variables. This generally relies upon the problem having some special form ... [69%] 2023-12-30 [Differential equations]
18. Stochastic partial differential equation: Stochastic partial differential equations (SPDEs) generalize partial differential equations via random force terms and coefficients, in the same way ordinary stochastic differential equations generalize ordinary differential equations. They have relevance to quantum field theory, statistical mechanics, and spatial modeling. [69%] 2023-12-30 [Stochastic differential equations] [Partial differential equations]...
19. Parabolic partial differential equation: A parabolic partial differential equation is a type of partial differential equation (PDE). Parabolic PDEs are used to describe a wide variety of time-dependent phenomena, including heat conduction, particle diffusion, and pricing of derivative investment instruments. (Class of second-order linear partial differential equations) [69%] 2023-12-30 [Parabolic partial differential equations]
20. Parabolic partial differential equation: An equation (cf. Differential equation, partial) of the form $$ u _ {t} - \sum _ { i,j=1}^n a _ {ij} ( x, t) u _ {x _ {i} x _ {j} } - \sum _ { i=1}^ { n } a _ {i} ( x ... (Mathematics) [69%] 2023-10-26