| Abstract: |
| In this talk, we propose a partial Newton-correction method (PNCM) to find multiple fixed points of nonlinear differential operators. First a new augmented singular transform is developed to form a barrier surrounding previously found or known fixed points so that an algorithm search from outside cannot pass the barrier and penetrate into the inside to reach a previously found fixed point. Thus a fixed point found by an algorithm must be new. Its mathematical validations are established. A flow chart of PNCM is presented. Then a more accurate Legendre-Gauss-Lobatto pseudospectral scheme is constructed to converte a nonlinear fixed point problem into a linear partial differential equation and an algebraic equation. It greatly simplifies the computation. Finally numerical results are presented to show the effectiveness of these approaches. Our approach is quite general and simple. It has a great potential to be modified to solve other multiple solution problems. |
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