Geodesic
Stability of explicit schemes for solving Maxwell's equations by high-order finite volume methods
Numerical methods and programming, Tome 15 (2014) no. 2, pp. 286-303

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A new stability criterion of explicit schemes for solving Maxwell's equations by high-order finite volume methods is proposed. The proof is based on a generalization of the stability criterion for the first-order finite volume scheme to the case of high-order schemes. The effect of discontinuities of the solution on the stability of high-order schemes is evaluated. The maximum principle for the finite volume approximations of vector conservation laws is discussed.
Keywords: Maxwell's equations, finite volume method, stability of explicit schemes, high-order accuracy, partial differential equations. 
@article{VMP_2014_15_2_a8,
     author = {D. K. Firsov},
     title = {Stability of explicit schemes for solving {Maxwell's} equations by high-order finite volume methods},
     journal = {Numerical methods and programming},
     pages = {286--303},
     publisher = {mathdoc},
     volume = {15},
     number = {2},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMP_2014_15_2_a8/}
}
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D. K. Firsov. Stability of explicit schemes for solving Maxwell's equations by high-order finite volume methods. Numerical methods and programming, Tome 15 (2014) no. 2, pp. 286-303. http://geodesic.mathdoc.fr/item/VMP_2014_15_2_a8/