ALGORITHMS AND VISUALIZATION FOR SOLUTIONS OF NONLINEAR ELLIPTIC EQUATIONS
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Publication:5474112
DOI10.1142/S0218127400001006zbMath1090.65549OpenAlexW1988400019MaRDI QIDQ5474112
Goong Chen, Wei-Ming Ni, Jian Xin Zhou
Publication date: 23 June 2006
Published in: International Journal of Bifurcation and Chaos (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1142/s0218127400001006
Multigrid methods; domain decomposition for boundary value problems involving PDEs (65N55) Nonlinear elliptic equations (35J60)
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Cites Work
- Unnamed Item
- Monotone explicit iterations of the finite element approximations for the nonlinear boundary value problem
- The effect of the domain topology on the number of positive solutions of nonlinear elliptic problems
- Initiation of slime mold aggregation viewed as an instability
- A nonlinear boundary value problem with many positive solutions
- The convergence of spline collocation for strongly elliptic equations on curves
- Finite difference approximations to the Dirichlet problem for elliptic systems
- The Chandrasekhar theory of stellar collapse as the limit quantum mechanics
- The effect of domain shape on the number of positive solutions of certain nonlinear equations
- Symmetry and related properties via the maximum principle
- Supersolutions, monotone iterations, and stability
- A finite element method for some integral equations of the first kind
- Traveling waves in a nonlinearly suspended beam: Theoretical results and numerical observations
- On the existence of sign changing solutions for semilinear Dirichlet problems
- Existence of many positive solutions of semilinear equations on annulus
- On the existence of positive entire solutions of a semilinear elliptic equation
- Dual variational methods in critical point theory and applications
- Mildly nonlinear elliptic partial differential equations and their numerical solution. II
- Numerical methods of high-order accuracy for nonlinear boundary value problems. I: One dimensional problem
- A high-linking algorithm for sign-changing solutions of semilinear elliptic equations
- Visualization of Special Eigenmode Shapes of a Vibrating Elliptical Membrane
- FURTHER STUDIES OF EMDEN'S AND SIMILAR DIFFERENTIAL EQUATIONS
- High-Order Finite Element Methods for Singularly Perturbed Elliptic and Parabolic Problems
- Multiple periodic solutions for a nonlinear suspension bridge equation
- Boundary element monotone iteration scheme for semilinear elliptic partial differential equations
- Boundary element monotone iteration scheme for semilinear elliptic partial differential equations, Part II: Quasimonotone iteration for coupled systems
- A mountain pass method for the numerical solution of semilinear elliptic problems
- On mildly nonlinear partial difference equations of elliptic type