Symmetric homotopy method for discretized elliptic equations with cubic and quintic nonlinearities
DOI10.1007/s10915-016-0284-8zbMath1373.65086OpenAlexW2523227026MaRDI QIDQ2356614
Bo Yu, JinTao Zhang, XuPing Zhang
Publication date: 6 June 2017
Published in: Journal of Scientific Computing (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s10915-016-0284-8
homotopy continuationnumerical experimentspolynomial systemboundary value problemmultiple solutionssemilinear elliptic equationeigenfunction expansionpolynomial nonlinearity
Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Completeness of eigenfunctions and eigenfunction expansions in context of PDEs (35P10) Global methods, including homotopy approaches to the numerical solution of nonlinear equations (65H20) Semilinear elliptic equations (35J61)
Related Items (2)
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Continuation along bifurcation branches for a tumor model with a necrotic core
- Proof of a conjecture on a discretized elliptic equation with cubic nonlinearity
- Bifurcation for a free boundary problem modeling the growth of a tumor with a necrotic core
- A three-dimensional steady-state tumor system
- Solution of polynomial systems derived from differential equations
- HOM4PS-2.0: a software package for solving polynomial systems by the polyhedral homotopy continuation method
- The random product homotopy and deficient polynomial systems
- Coefficient-parameter polynomial continuation
- Quantization effects for \(-\Delta u=u(1-| u|^ 2)\) in \(\mathbb{R}^ 2\)
- Symmetric homotopy construction
- Search extension method for multiple solutions of a nonlinear problem
- A bootstrapping approach for computing multiple solutions of differential equations
- A Minimax Method for Finding Multiple Critical Points and Its Applications to Semilinear PDEs
- Eigenfunction Expansion Method for Multiple Solutions of Semilinear Elliptic Equations with Polynomial Nonlinearity
- Numerical algebraic geometry and algebraic kinematics
- A Hybrid Polynomial System Solving Method for Mixed Trigonometric Polynomial Systems
- A high-linking algorithm for sign-changing solutions of semilinear elliptic equations
- Algorithm 795
- Application of numerical continuation to compute all solutions of semilinear elliptic equations
- A mountain pass method for the numerical solution of semilinear elliptic problems
- Symmetry and Automated Branch Following for a Semilinear Elliptic PDE on a Fractal Region
- The Numerical Solution of Systems of Polynomials Arising in Engineering and Science
- An improved search-extension method for computing multiple solutions of semilinear PDEs
- NEWTON'S METHOD AND MORSE INDEX FOR SEMILINEAR ELLIPTIC PDEs
This page was built for publication: Symmetric homotopy method for discretized elliptic equations with cubic and quintic nonlinearities
