In this paper a one parameter predictor–corrector method, which we call it A-EBDF, is introduced and analyzed. With a modification of A-BDF and EBDF methods we propose a multistep method whose region of absolute stability is larger than those of A-BDF and EBDF methods. © 2004 IMACS. Published by Elsevier B.V. All rights reserved. MSC: 65L05

The paper extends prior work by the authors on LOQO, an interior point algorithm for nonconvex nonlinear programming. The specific topics covered include primal versus dual orderings and higher order methods, which attempt to use each factorization of the Hessian matrix more than once to improve computational efficiency. Results show that unlike linear and convex quadratic programming, higher o...

We discuss a procedure for numerically approximating solutions to a system of nonlinear partial diierential equations which describe mountain pine beetles attacking lodgepole pine en masse. A centered spatial dicretization which yields a system of ordinary diierential equations is presented, including a method for generating`trans-parent' spatial boundary conditions. A ux-based model estimates ...

In this paper, the sharp interface, direct forcing immersed boundary method developed by Yang and Stern (A simple and efficient direct forcing immersed boundary framework for fluidstructure interactions, J. Comput. Phys. 231 (2012) 5029-5061) is applied to the fully resolved simulation of particulate flow. This method uses a discrete forcing approach and maintains a sharp profile of the fluid/s...

page 1 Predictor Corrector Methods Predictor Corrector Methods form the basis of the most successful codes (Variable Step Variable Order Methods) for the solution of initial value problems of ordinary differential equations. Briefly, these methods have been successful because they occur in naturally arising families covering a range of orders, they have reasonable stability properties, and they...

In this paper, we proposed a simple modification of McDougall and Wotherspoon [11] method for approximating the root of univariate function. Our modification is based on the approximating the derivative in the corrector step of the proposed McDougall and Wotherspoon Newton like method using secant method. Numerical examples demonstrate the efficiency of the proposed method.

A family of Enright’s second derivative formulas with trigonometric basis functions is derived using multistep collocation method. The continuous schemes obtained are used to generate complementary methods. The stability properties of the methods are discussed.Themethodswhich can be applied in predictor-corrector formare implemented in block formas simultaneous numerical integrators over nonove...

This paper addresses the role of centrality in the implementation of interior point methods. We provide theoretical arguments to justify the use of a symmetric neighbourhood, and translate them into computational practice leading to a new insight into the role of recentering in the implementation of interior point methods. Second-order correctors, such as Mehrotra’s predictor–corrector, can occ...