A degree-increasing [\(N\)~to~\(N+1\)] homotopy for Chebyshev and Fourier spectral methods

DOI10.1016/j.aml.2016.01.001zbMath1334.65122OpenAlexW2269132390MaRDI QIDQ253919

John P. Boyd

Publication date: 8 March 2016

Published in: Applied Mathematics Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aml.2016.01.001

zbMATH Keywords

convergenceChebyshev polynomialsnonlinear differential equationsfinite differencehomotopycontinuationNewton's iterationGröbner basis methodpseudospectralspectral Galerkin algorithm

Mathematics Subject Classification ID

Nonlinear boundary value problems for ordinary differential equations (34B15) Global methods, including homotopy approaches to the numerical solution of nonlinear equations (65H20) Stability and convergence of numerical methods for ordinary differential equations (65L20) Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60) Error bounds for numerical methods for ordinary differential equations (65L70) Finite difference and finite volume methods for ordinary differential equations (65L12)

Related Items

Tracing multiple solution branches for nonlinear ordinary differential equations: Chebyshev and Fourier spectral methods and a degree-increasing spectral homotopy [DISH], Two-Level Spectral Methods for Nonlinear Elliptic Equations with Multiple Solutions, All roots spectral methods: constraints, floating point arithmetic and root exclusion

Cites Work

• Solution of polynomial systems derived from differential equations
• Modeling nonlinear resonance: A modification to the Stokes' perturbation expansion
• Solving Transcendental Equations
• On Solving Nonlinear Equations with a One-Parameter Operator Imbedding