A series of compact implicit schemes of fourth and sixth orders are developed for solving differential equations involved in geodynamics simulations. Three illustrative examples are described to demonstrate that high-order convergence rates are achieved while good efficiency in terms of fewer grid points is maintained. This study shows that high-order compact implicit difference methods provide...

We present and implement a fourth-order projective dependency parsing algorithm that effectively utilizes both “grand-sibling” style and “tri-sibling” style interactions of third-order and “grand-tri-sibling” style interactions of forth-order factored parts for performance enhancement. This algorithm requires O(n5) time and O(n4) space. We implement and evaluate the parser on two languages—Engl...

In many problems, one wishes to solve the Helmholtz equation in cylindrical or spherical coordinates which introduces variable coefficients within the differentiated terms. Fourth order accurate methods are desirable to reduce pollution and dispersion errors and so alleviate the points-per-wavelength constraint. However, the variable coefficients renders existing fourth order finite difference ...

In this paper, an iterative scheme is proposed to find the roots of a nonlinear equation. It is shown that this iterative method has fourth order convergence in the neighborhood of the root. Based on this iterative scheme, we propose the main contribution of this paper as a new high-order computational algorithm for finding an approximate inverse of a square matrix. The analytical discussions s...

Darvishi and Barati [M.T. Darvishi, A. Barati, Super cubic iterative methods to solve systems of nonlinear equations, Appl. Math. Comput., 2006, 10.1016/j.amc.2006.11.022] derived a Super cubic method from the Adomian decomposition method to solve systems of nonlinear equations. The authors showed that the method is third-order convergent using classical Taylor expansion but the numerical exper...

In this paper we present an explicit fourth-order method for the integration of Hamilton’s Equations. This method preserves the property that the time evolution of such a system yields a canonical transformation from the initial conditions to the final state. That is, the integration step is an explicit symplectic map. Although the result is first derived for a specific type of Hamiltonian, it ...

In an earlier publication, the authors reported the successful solution of the Fokker-Planck equation by the finite element method for a class of second order systems subjected to both additive and multiplicative white noise excitations, giving a complete picture of the evolution of the transition probability density functions of those systems. More recently, these solutions have been used to d...