Block Monotone Iterative Method for Semilinear Parabolic Equations with Nonlinear Boundary Conditions
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Summary
It is shown that by using an upper solution and a lower solution as initial iterations each of the iterative schemes yields two sequences which converge monotonically from above and below, respectively, to a unique solution of the finite difference system.
- Type
- article
- Published
- 2010-01-01
- Cited by
- 17
- References
- 32
- OpenAlex
- https://openalex.org/W1986306555
- Semantic Scholar
- https://api.semanticscholar.org/CorpusID:207059022
Keywords
Mathematics, Monotone polygon, Nonlinear system, Iterative method, Boundary value problem
References
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- Nonlinear parabolic and elliptic equations
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- Monotone iterative methods for the adaptive finite element solution of semiconductor equations
- Monotone scheme for finite difference equations concerning steady-state prey-predator interactions☆
- A block monotone domain decomposition algorithm for a semilinear convection-diffusion problem
- Stabilized Explicit-Implicit Domain Decomposition Methods for the Numerical Solution of Parabolic Equations
- Mildly nonlinear elliptic partial differential equations and their numerical solutoin. II
- Numerical Methods for Semilinear Parabolic Equations
- Monotone iterative methods for finite difference system of reaction-diffusion equations
- On linear monotone iteration and Schwarz methods for nonlinear elliptic PDEs
- Blowing-up and asymptotic behaviour of solutions for a finite difference system
- Block Monotone Iterations for Numerical Solutions of Fourth-Order Nonlinear Elliptic Boundary Value Problems
- Numerical Methods for Singular Boundary Value Problems
- Iterative Solution of Large Linear Systems.
- Numerical methods for fourth‐order nonlinear elliptic boundary value problems
- Monotone explicit iterations of the finite element approximations for the nonlinear boundary value problem
- On the Schwarz alternating method with more than two subdomains for nonlinear monotone problems
- Monotone method and convergence acceleration for finite‐difference solutions of parabolic problems with time delays
Cited by
- Monotone iterates for solving nonlinear integro-parabolic equations of Volterra type
- Permanence and coexistence in a diffusive complex ratio-dependent food chain
- Finite difference methods for a nonlinear and strongly coupled heat and moisture transport system in textile materials
- Inexact block monotone methods for solving nonlinear elliptic problems
- An inexact monotone method for solving semilinear parabolic problems
- Convergence Analysis of an Iterative Method for Nonlinear Partial Differential Equations
- Numerical solving nonlinear integro-parabolic equations by the monotone weighted average method
- A NUMERICAL METHOD FOR SOLVING NONLINEAR INTEGRO-DIFFERENTIAL EQUATIONS OF FREDHOLM TYPE
- Coupling hyperbolic and parabolic equations
- Numerical simulation of porous silicon morphology using a monotone iterative method
- Error analysis for time-fractional semilinear parabolic equations using upper and lower solutions
- Asymptotic behavior of reaction–advection–diffusion population models with Allee effect
- Convergence, stability analysis, and solvers for approximating sublinear positone and semipositone boundary value problems using finite difference methods
- Numerical solution of nonlinear parabolic systems by block monotone methods
- New Contribution to the Advancement of Fixed Point Theory, Equilibrium Problems, and Optimization Problems
- On models of shared resource competition, coexistence and traveling waves.
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