Eigenfunction Expansion Method for Multiple Solutions of Semilinear Elliptic Equations with Polynomial Nonlinearity

DOI10.1137/12088327XzbMath1305.65174MaRDI QIDQ2870623

Bo Yu, XuPing Zhang, JinTao Zhang

Publication date: 21 January 2014

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

zbMATH Keywords

homotopy continuationerror analysisspurious solutionpolynomial systemsemilinear elliptic equationeigenfunction expansion discretization

Mathematics Subject Classification ID

Numerical computation of solutions to systems of equations (65H10) Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Numerical solution of boundary value problems involving ordinary differential equations (65L10)

Related Items (7)

Two-Level Spectral Methods for Nonlinear Elliptic Equations with Multiple Solutions ⋮ Finding multiple solutions to elliptic systems with polynomial nonlinearity ⋮ An efficient spectral trust-region deflation method for multiple solutions ⋮ Eigenfunction expansion method for multiple solutions of fourth-order ordinary differential equations with cubic polynomial nonlinearity ⋮ A homotopy method with adaptive basis selection for computing multiple solutions of differential equations ⋮ Convergence, stability analysis, and solvers for approximating sublinear positone and semipositone boundary value problems using finite difference methods ⋮ Symmetric homotopy method for discretized elliptic equations with cubic and quintic nonlinearities

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