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A quasilinearization method for elliptic problems with a nonlinear boundary condition

✍ Scribed by P. Amster; P. De Nápoli

Publisher
Elsevier Science
Year
2007
Tongue
English
Weight
161 KB
Volume
66
Category
Article
ISSN
0362-546X

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✦ Synopsis

We study a nonlinear elliptic second order problem with a nonlinear boundary condition. Assuming the existence of an ordered couple of a supersolution and a subsolution, we develop a quasilinearization method in order to construct an iterative scheme that converges to a solution. Furthermore, under an extra assumption we prove that the convergence is quadratic.

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Materials which are heated by the passage of electricity are usually modeled by a nonlinear coupled system of two partial differential equations. The current equation is elliptic, while the temperature equation is parabolic. These equations are coupled one to another through the conductivities and t