Iterative methods and high-order difference schemes for 2D elliptic problems with mixed derivative

High-order numerical schemes based on difference potentials for 2D elliptic problems with material interfaces

Article history: Received 11 February 2016 Received in revised form 13 July 2016 Accepted 30 August 2016 Available online 8 September 2016

Higher-Order Difference and Higher-Order Splitting Methods for 2D Parabolic Problems with Mixed Derivatives

In this article we discuss a combination between fourth-order finite difference methods and fourth-order splitting methods for 2D parabolic problems with mixed derivatives. The finite difference methods are based on higher-order spatial discretization methods, whereas the timediscretization methods are higher-order discretizations using CrankNicolson or BDF methods. The splitting methods are hi...

Multilevel Preconditioners for Mixed Methods for Second Order Elliptic Problems

A new approach of constructing algebraic multilevel preconditioners for mixed nite element methods for second order elliptic problems with tensor coe cients on general geometry is proposed The linear system arising from the mixed methods is rst algebraically condensed to a symmetric positive de nite system for Lagrange multipliers which corresponds to a linear system generated by standard nonco...

Higher Order Derivative Estimates for Finite-difference Schemes for Linear Elliptic and Parabolic Equations

THIRD-ORDER AND FOURTH-ORDER ITERATIVE METHODS FREE FROM SECOND DERIVATIVE FOR FINDING MULTIPLE ROOTS OF NONLINEAR EQUATIONS

In this paper, we present two new families of third-order and fourth-order methods for finding multiple roots of nonlinear equations. Each of them requires one evaluation of the function and two of its first derivative per iteration. Several numerical examples are given to illustrate the performance of the presented methods.