Partial-Differential Equations

Clemens Heitzinger ()
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Clemens Heitzinger: Technische Universität Wien, Center for Artificial Intelligence and Machine Learning (CAIML) and Department of Mathematics and Geoinformation

Chapter Chapter 10 in Algorithms with JULIA, 2022, pp 257-304 from Springer

Abstract: Abstract Partial-differential equations are equations that contain partial derivatives of the unknown function. The field of partial-differential equations is large and diverse, as these equations describe many different phenomena and systems, and hence many theories for the existence and uniqueness of their solutions as well as many numerical methods have been developed. In this chapter, we explain fundamental concepts and numerical methods using the example of three important classes of partial-differential equations, namely elliptic, parabolic, and hyperbolic. These types of equations describe diverse physical phenomena such as diffusion, thermal conduction, electromagnetism, and wave propagation. Finite differences, finite volumes, and finite elements are used to calculate approximations of the solutions.

Date: 2022
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DOI: 10.1007/978-3-031-16560-3_10

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