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t. e. 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 thought of as an unknown number to be solved for in an algebraic equation like x2 − 3x + 2 = 0.
e. In mathematics, the method of characteristics is a technique for solving partial differential equations. Typically, it applies to first-order equations, although more generally the method of characteristics is valid for any hyperbolic and parabolic partial differential equation.
Free boundary problem. In mathematics, a free boundary problem (FB problem) is a partial differential equation to be solved for both an unknown function and an unknown domain . The segment of the boundary of which is not known at the outset of the problem is the free boundary. FBs arise in various mathematical models encompassing applications ...
List of finite element software packages. This is a list of notable software packages that implement the finite element method for solving partial differential equations. FEA, Multi-physics, Implict & Explict. It is an Open Source FEA project. The solver uses a partially compatible ABAQUS file format.
The boundary element method (BEM) is a numerical computational method of solving linear partial differential equations which have been formulated as integral equations (i.e. in boundary integral form), including fluid mechanics, acoustics, electromagnetics (where the technique is known as method of moments or abbreviated as MoM), [1] fracture mechanics, [2] and contact mechanics.
The Feynman–Kac formula, named after Richard Feynman and Mark Kac, establishes a link between parabolic partial differential equations and stochastic processes.In 1947, when Kac and Feynman were both faculty members at Cornell University, Kac attended a presentation of Feynman's and remarked that the two of them were working on the same thing from different directions. [1]
Pseudo-spectral method. Pseudo-spectral methods, [1] also known as discrete variable representation (DVR) methods, are a class of numerical methods used in applied mathematics and scientific computing for the solution of partial differential equations. They are closely related to spectral methods, but complement the basis by an additional ...
Lax–Friedrichs method. The Lax–Friedrichs method, named after Peter Lax and Kurt O. Friedrichs, is a numerical method for the solution of hyperbolic partial differential equations based on finite differences. The method can be described as the FTCS (forward in time, centered in space) scheme with a numerical dissipation term of 1/2.
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