CONVERGENCE CRITERIA FOR SYSTEMS OF NON-LINEAR ELLIPTIC PARTIAL DIFFERENTIAL EQUATIONS
Abstract
This thesis deals with convergence criteria for a special system of non-linear elliptic partial differential equations. A fixed point algorithm is used, which iteratively solves one linearized elliptic partial differential equation at a time. We establish conditions which help foresee the convergence of the algorithm. We prove, under reasonable hypotheses, that the algorithm converges for such non-linear elliptic systems. Extensive experimental results are reported and they show the algorithm converges in a wide variety of cases and the convergence is well correlated with the theoretical conditions introduced in this thesis.
Degree
Ph.D.
Subject Area
Mathematics
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