Monolithic, non-iterative and iterative time discretization methods for linear coupled elliptic-parabolic systems

Iterative methods for solving non linear Fokker-Planck equation

On the modified iterative methods for $M$-matrix linear systems

This paper deals with scrutinizing the convergence properties of iterative methods to solve linear system of equations. Recently, several types of the preconditioners have been applied for ameliorating the rate of convergence of the Accelerated Overrelaxation (AOR) method. In this paper, we study the applicability of a general class of the preconditioned iterative methods under certain conditio...

Iterative Methods for Linear Systems

This chapter contains an overview of some of the important techniques used to solve linear systems of equations Ax = b (1) by iterative methods. We consider methods based on two general ideas, splittings of the coeecient matrix, leading to stationary iterative methods, and Krylov subspace methods. These two ideas can also be combined to produce preconditioned iterative methods. In addition, we ...

Iterative Methods for Linear Systems

In many applications we have to solve a linear system Ax = b with A ∈ Rn×n and b ∈ Rn given. If n is large the solution of the linear system takes a lot of operations, and standard Gaussian elimination may take too long. But in many cases most entries of the matrix A are zero and A is a so-called sparse matrix. This means each equation only couples very few of the n unknowns x1, . . . , xn. A t...

Iterative methods for linear systems

For many elliptic PDE problems, finite-difference and finite-element methods are the techniques of choice. In a finite-difference approach, a solution uk on a set of discrete gridpoints 1, . . . , k is searched for. The discretized partial differential equation and boundary conditions create linear relationships between the different values of uk. In the finite-element method, the solution is e...