Boundary Value Problems and Iterative Methods for Linear Systems
ثبت نشده
چکیده
1.1. Abstract setting We want to find a “displacement” u ∈ V . Here V is a complete vector space with a norm ‖v‖V . In the absence of external forces the equilibrium solution minizes the “internal energy” Q(u). If there are external forces: Now changing the displacement from u to u+ v corresponds to a work `(v) (“work of external forces”). Here ` : V → R is linear and bounded: ∀v ∈ V : |`(v)| ≤ C` ‖v‖
منابع مشابه
On Approximate Stationary Radial Solutions for a Class of Boundary Value Problems Arising in Epitaxial Growth Theory
In this paper, we consider a non-self-adjoint, singular, nonlinear fourth order boundary value problem which arises in the theory of epitaxial growth. It is possible to reduce the fourth order equation to a singular boundary value problem of second order given by w''-1/r w'=w^2/(2r^2 )+1/2 λ r^2. The problem depends on the parameter λ and admits multiple solutions. Therefore, it is difficult to...
متن کاملA Consistent and Accurate Numerical Method for Approximate Numerical Solution of Two Point Boundary Value Problems
In this article we have proposed an accurate finite difference method for approximate numerical solution of second order boundary value problem with Dirichlet boundary conditions. There are numerous numerical methods for solving these boundary value problems. Some these methods are more efficient and accurate than others with some advantages and disadvantages. The results in experiment on model...
متن کاملParallel Iterative Solvers for Boundary Value Methods
A parallel variant of the block Gauss-Seidel iteration for the solution of block-banded linear systems is presented. The coefficient matrix is partitioned among the processors ss in the domain decomposition methods and then it is split so that the resulting iterative method has the same spectral properties of the block Gauss-Seidel iteration. The parallel algorithm is applied to the solution of...
متن کاملAugmented Lagrangian method for solving absolute value equation and its application in two-point boundary value problems
One of the most important topic that consider in recent years by researcher is absolute value equation (AVE). The absolute value equation seems to be a useful tool in optimization since it subsumes the linear complementarity problem and thus also linear programming and convex quadratic programming. This paper introduce a new method for solving absolute value equation. To do this, we transform a...
متن کاملFast iterative solvers for boundary value problems on a local spherical region
Boundary value problems on local spherical regions arise naturally in geophysics and oceanography when scientists model a physical quantity on large scales. Meshless methods using radial basis functions (rbfs) provide a simple way to construct numerical solutions with high accuracy. However, the linear systems arising from these methods are usually ill-conditioned, which poses a challenge for i...
متن کاملIntroduction to Multigrid Methods for Elliptic Boundary Value Problems
We treat multigrid methods for the efficient iterative solution of discretized elliptic boundary value problems. Two model problems are the Poisson equation and the Stokes problem. For the discretization we use standard finite element spaces. After discretization one obtains a large sparse linear system of equations. We explain multigrid methods for the solution of these linear systems. The bas...
متن کامل