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Finite difference scheme to a nonlinear integro-differential equation associated with the penetration of a magnetic field into a substance. (English) Zbl 1338.78026

Botchorishvili, Ramaz (ed.) et al., Finite differences, finite elements, finite volumes, boundary elements. Proceedings of the 2nd WSEAS international conference on finite differences, finite elements, finite volumes, boundary elements, Tbilisi, Georgia, June 26–28, 2009. Athens: WSEAS Press (ISBN 978-960-474-089-5/hbk; 978-960-474-090-1/cd-rom). Mathematics and Computers in Science and Engineering, 186-192 (2009).
Summary: Finite difference approximation of the nonlinear integro-differential equation associated with the penetration of a magnetic field into a substance is studied. Initial-boundary value problems with homogeneous as well as nonhomogeneous Dirichlet boundary conditions are considered. The convergence of the finite difference scheme is proven. The rate of convergence is given too. Numerical experiments are carried out.
For the entire collection see [Zbl 1205.00079].

MSC:

78M20 Finite difference methods applied to problems in optics and electromagnetic theory
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