Finite difference approximations are methods for solving differential equations by approximating derivatives. This work will begin with how to solve a partial differential equation (PDE) called the advection equation, ut + cux = 0. Both analytically, and approximately with three different finite difference methods for the spatial part of the equation: • Central in space, • First order upwind in space, • Beam-Warming in space, and forward Euler for the temporal part. We then use the theoretical approximations considered for the advection equation and apply it on Maxwell’s equations for electromagnetism in 1D. This is a system of advection equations that describes how electromagnetic waves propagate through a dielectric material. In the end of this work we will model this electromagnetic wave, or wave of light moving through materials with different refraction indexes.
| Identifer | oai:union.ndltd.org:UPSALLA1/oai:DiVA.org:liu-185516 |
| Date | January 2022 |
| Creators | Lindqvist, Sebastian |
| Publisher | Linköpings universitet, Tillämpad matematik, Linköpings universitet, Tekniska fakulteten |
| Source Sets | DiVA Archive at Upsalla University |
| Language | English |
| Detected Language | English |
| Type | Student thesis, info:eu-repo/semantics/bachelorThesis, text |
| Format | application/pdf |
| Rights | info:eu-repo/semantics/openAccess |
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