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In mathematics, a partial differential equation (PDE) is an equation which involves a multivariable function and one or more of its partial derivatives.. The function is often thought of as an "unknown" that solves the equation, similar to how x is thought of as an unknown number solving, e.g., an algebraic equation like x 2 − 3x + 2 = 0.
Please introduce links to this page from ; try the Find link tool for suggestions. ( November 2016 ) The mathematical analysis of partial differential equations uses analytical techniques to study partial differential equations .
US-based and -developed full CAE software package: Ansys Inc. 2022 R2: 2022-07-28: Proprietary commercial software: Free student version available, up to 32,000 nodes/elements [9] Windows, Linux: COMSOL Multiphysics: COMSOL Multiphysics Finite Element Analysis Software (formerly FEMLAB) COMSOL Inc. 6.1: 2022-11-01: Proprietary EULA: Linux, Mac ...
In mathematics, and more precisely, in functional Analysis and PDEs, the Schauder estimates are a collection of results due to Juliusz Schauder (1934, 1937) concerning the regularity of solutions to linear, uniformly elliptic partial differential equations.
FEATool Multiphysics is a fully integrated physics and PDE simulation environment where the modeling process is subdivided into six steps; preprocessing (CAD and geometry modeling), mesh and grid generation, physics and PDE specification, boundary condition specification, solution, and postprocessing and visualization.
Name Dim Equation Applications Landau–Lifshitz model: 1+n = + Magnetic field in solids Lin–Tsien equation: 1+2 + = Liouville equation: any + = Liouville–Bratu–Gelfand equation
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Broer–Kaup equations; Burgers' equation; Euler equations; Fokker–Planck equation; Hamilton–Jacobi equation, Hamilton–Jacobi–Bellman equation; Heat equation; Laplace's equation