Monotone Iterates with Quadratic Convergence Rate for Solving Semilinear Parabolic Problems
نویسندگان
چکیده
This paper deals with numerical solving semilinear parabolic problems based on the method of upper and lower solutions. A monotone iterative method with quadratic convergence rate is constructed. The monotone iterative method combines an explicit construction of initial upper and lower solutions and the modified accelerated monotone iterative method. The monotone iterative method leads to the existence-uniqueness theorem. An analysis of convergence rates of the monotone iterative method, based on different stoping tests, is given. Results of numerical experiments are presented, where iteration counts are compared with a monotone iterative method, whose convergence rate is linear.
منابع مشابه
Uniform Quadratic Convergence of a Monotone Weighted Average Method for Semilinear Singularly Perturbed Parabolic Problems
This paper deals with a monotone weighted average iterative method for solving semilinear singularly perturbed parabolic problems. Monotone sequences, based on the accelerated monotone iterative method, are constructed for a nonlinear difference scheme which approximates the semilinear parabolic problem. This monotone convergence leads to the existence-uniqueness theorem. An analysis of uniform...
متن کاملQuadratic convergence of monotone iterates for semilinear elliptic obstacle problems
In this paper, we consider the numerical solution for the discretization of semilinear elliptic complementarity problems. A monotone algorithm is established based on the upper and lower solutions of the problem. It is proved that iterates, generated by the algorithm, are a pair of upper and lower solution iterates and converge monotonically from above and below, respectively, to the solution o...
متن کاملMonotone Relaxation Iterates and Applications to Semilinear Singularly Perturbed Problems
This paper deals with monotone relaxation iterates for solving nonlinear monotone difference schemes of elliptic type. The monotone ω-Jacobi and SUR (Successive Under-Relaxation) methods are constructed. The monotone methods solve only linear discrete systems at each iterative step and converge monotonically to the exact solution of the nonlinear monotone difference schemes. Convergent rates of...
متن کاملThe Generalized Quasilinearization Method for Parabolic Integro-differential Equations
In this paper we consider the nonlinear parabolic integro-differential equation with initial and boundary conditions. We develop the method of generalized quasilinearization to generate linear iterates that converge quadratically to the unique solution of the nonlinear parabolic integro-differential equation. For this purpose, we establish comparison results for the parabolic integro-differenti...
متن کاملBoundary element monotone iteration scheme for semilinear elliptic partial differential equations
The monotone iteration scheme is a constructive method for solving a wide class of semilinear elliptic boundary value problems. With the availability of a supersolution and a subsolution, the iterates converge monotonically to one or two solutions of the nonlinear PDE. However, the rates of such monotone convergence cannot be determined in general. In addition, when the monotone iteration schem...
متن کامل