Block Monotone Iterations for Numerical Solutions of Fourth-Order Nonlinear Elliptic Boundary Value Problems
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Summary
It is shown that the sequence of iterations converges monotonically to a maximal solution or a minimal solution if the nonlinear function is quasi-monotone nondecreasing and that the finite difference solution converges to the continuous solution as the mesh size tends to zero.
- Type
- article
- Published
- 2003-01-01
- Cited by
- 29
- References
- 27
- OpenAlex
- https://openalex.org/W2040665934
- Semantic Scholar
- https://api.semanticscholar.org/CorpusID:21053008
Keywords
Mathematics, Monotone polygon, Discretization, Boundary value problem, Nonlinear system
References
- Theory of Elastic Stability
- On fourth order boundary value problems arising in beam analysis
- Nonlinear parabolic and elliptic equations
- On fourth-order elliptic boundary value problems
- The Theory of critical phenomena
- Numerical solutions for some coupled systems of nonlinear boundary value problems
- The Method of Lower and Upper Solutions for Fourth-Order Two-Point Boundary Value Problems
- Fourth-order two-point boundary value problems
- Existence and uniqueness theorems for the bending of an elastic beam equation
- Monotone scheme for finite difference equations concerning steady-state prey-predator interactions☆
- Mildly nonlinear elliptic partial differential equations and their numerical solutoin. II
- A uniqueness theorem for a boundary value problem
- On the Existence of Positive Solutions of Fourth-Order Ordinary Differential Equations
- Application of the renormalization group to phase transitions in disordered systems
- Full-Order Convergence of a Mixed Finite Element Method for Fourth-Order Elliptic Equations
- The Method of Lower and Upper Solutions for Second, Third, Fourth, and Higher Order Boundary Value Problems
- Numerical Methods for Singular Boundary Value Problems
- Monotone explicit iterations of the finite element approximations for the nonlinear boundary value problem
- Monotone method and convergence acceleration for finite‐difference solutions of parabolic problems with time delays
- Block monotone iterative methods for numerical solutions of nonlinear elliptic equations
Cited by
- Nonlinear fourth-order elliptic equations with nonlocal boundary conditions
- A Finite Difference Method and Analysis for 2D Nonlinear Poisson–Boltzmann Equations
- Block Monotone Iterative Method for Semilinear Parabolic Equations with Nonlinear Boundary Conditions
- A block monotone iterative method for numerical solutions of nonlinear elliptic boundary value problems
- Fourth-order compact finite difference method for fourth-order nonlinear elliptic boundary value problems
- Convergence analysis of a monotone method for fourth-order semilinear elliptic boundary value problems
- On fourth-order elliptic boundary value problems with nonmonotone nonlinear function☆
- A fourth-order compact finite difference method for higher-order Lidstone boundary value problems
- Error and stability of monotone method for numerical solutions of fourth-order semilinear elliptic boundary value problems
- Optimal error estimates of mixed finite element methods for a fourth-order nonlinear elliptic problem
- A survey on various computational techniques for nonlinear elliptic boundary value problems
- Monotone iterative technique for numerical solutions of fourth-order nonlinear elliptic boundary value problems
- A ROBUST HIGH-ORDER COMPACT METHOD FOR THE THREE DIMENSIONAL NONLINEAR BIHARMONIC EQUATIONS
- A new coupled high-order compact method for the three-dimensional nonlinear biharmonic equations
- Numerical methods for fourth-order elliptic equations with nonlocal boundary conditions
- On existence of wavefront solutions in mixed monotone reaction-diffusion systems
- Error analysis of a compact finite difference method for fourth-order nonlinear elliptic boundary value problems
- A Monotone Iterative Technique for Nonlinear Fourth Order Elliptic Equations with Nonlocal Boundary Conditions
- Wavefront solutions of quasilinear reaction–diffusion systems with mixed quasi-monotonicity
- Block monotone iterative methods for solving coupled systems of nonlinear elliptic problems
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