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Showing content from http://reference.wolfram.com/language/PDEModels/tutorial/PDEModelsOverview.html below:

PDEModels Overview—Wolfram Language Documentation

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PDE MODELS OVERVIEW This partial differential equation (PDE) model overview provides a starting point for setting up PDE models in various fields of physics. The PDE models presented here are based on a high-level PDE modeling language expressed through PDEComponent functions and boundary Conditions and Values. It is important to realize that in case your field of interest is not presented here, that does by not mean that the Wolfram Language cannot solve equations from that field; it just means that these differential equations need to expressed in a more mathematical notation detailed in the guide pages for Differential Operators, Differential Equations and Partial Differential Equations.

This tutorial, in contrast, provides an overview over which fields of physics have a high-level representation in the Wolfram Language. The various fields presented here have a varying degree of completeness. Again, if a specific equation is not presented here, it does not mean that it cannot be solved; it just means there is no high-level representation yet. Future versions of the Wolfram Language will continue to expand in this area.

Typically, a field of physics that is considered complete consists of a guide page specific to that area and one or more monographs explaining the theory behind the functions provided. In some cases, verification notebooks are provided. A collection on models provides extended examples that showcase a specific application. The application models are typically more extensive then what one would normally find in the reference documentation. The example collection points to examples from the reference documentation that show a feature of particular interest.

The PDEs and boundary conditions guide page of a specific field of physics will link to a guide page that provides a listing of all available PDE functions and boundary conditions that are useful for creating PDE models in that area. A short description of the various PDE models can also be found on the guide page, and a more detailed overview of which model makes use of which functionality is provided last.

Acoustics Electromagnetics Electromagnetics Examples Fluid Dynamics Heat Transfer Mass Transport Multiphysics Physics SystemPhysics Structural Mechanics Structural Mechanics Models Structural Mechanics Examples The Finite Element Method

The finite element method is a solution method for partial differential equations and the main method to solve the PDE models presented here. More information on the finite element method is found in the following guide and overview page.

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