Journal of Computational and Applied Mathematics
Numerical estimates for semilinear parabolic equations
SIAM Journal on Numerical Analysis
On the Schwarz alternating method with more than two subdomains for nonlinear monotone problems
SIAM Journal on Numerical Analysis
Boundary element monotone iteration scheme for semilinear elliptic partial differential equations
Mathematics of Computation
Block monotone iterative methods for elliptic variational inequatlities
Applied Mathematics and Computation
SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
Monotone iterative methods for the adaptive finite element solution of semiconductor equations
Journal of Computational and Applied Mathematics
An Implicit-Explicit Runge--Kutta--Chebyshev Scheme for Diffusion-Reaction Equations
SIAM Journal on Scientific Computing
A block monotone domain decomposition algorithm for a semilinear convection-diffusion problem
Journal of Computational and Applied Mathematics
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Two block monotone iterative schemes, called Jacobi and Gauss-Seidel monotone iterations, are presented for numerical solutions of a class of semilinear parabolic equations under nonlinear boundary conditions by the finite difference method. These iteration schemes extend the method for semilinear elliptic boundary value problems to parabolic equations, including a comparison result between them. 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. Some error estimates and a convergence theorem are given, and various sufficient conditions for the construction of upper and lower solutions are obtained. Numerical results are presented for some physical model problems, including some problems with known continuous solutions and two problems with L-shaped and trapezoidal domains.