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Journal of Scientific Computing
Erschienen in: Journal of Scientific Computing 2/2023

01.11.2023

Partial Newton-Correction Method for Multiple Fixed Points of Semi-linear Differential Operators by Legendre–Gauss–Lobatto Pseudospectral Method

verfasst von: Zhaoxiang Li, Feng Zhang, Jianxin Zhou

Erschienen in: Journal of Scientific Computing | Ausgabe 2/2023

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Abstract

Inspired by several numerical methods for finding multiple solutions, a partial Newton-correction method (PNCM) is proposed to find multiple fixed points of semi-linear differential operators. First a new augmented singular transform is developed to form a barrier so that an algorithm search outside the subspace generated by previously found fixed points cannot pass the barrier and penetrate into the inside to reach an old 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 and convertes a semi-linear 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.
Vorheriger Artikel A Modified A Posteriori Subcell Limiter for High Order Flux Reconstruction Scheme for One-Dimensional Detonation Simulation
Nächster Artikel Implicit Integration of Nonlinear Evolution Equations on Tensor Manifolds

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Metadaten
Titel
Partial Newton-Correction Method for Multiple Fixed Points of Semi-linear Differential Operators by Legendre–Gauss–Lobatto Pseudospectral Method
verfasst von
Zhaoxiang Li
Feng Zhang
Jianxin Zhou
Publikationsdatum
01.11.2023
Verlag
Springer US
Erschienen in
Journal of Scientific Computing / Ausgabe 2/2023
Print ISSN: 0885-7474
Elektronische ISSN: 1573-7691
DOI
https://doi.org/10.1007/s10915-023-02341-z

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