One of the most efficient methods for determining the equilibria of a continuous parameterized family of differential equations is to use predictor-corrector continuation techniques. In the case of partial differential equations this procedure must be applied to some finite dimensional approximation which of course raises the question of the validity of the output. We introduce a new technique ...

I came up with the name TECO in 1962 while sitting in Ye Hong Guey, my favorite restaurant in Boston’s Chinatown during my undergraduate years at the Massachusetts Institute of Technology. I had been working on a little program to help me write other programs, a common activity in the day when a computer (the Digital Equipment Corporation PDP-1) would be delivered with almost no software. My pr...

We examine the stability properties of a predictor-corrector implementation of a class of implicit linear multistep methods. The method has recently been described in the literature as suitable for the efficient integration of stiff systems and as having stability regions similar to well known implicit methods. A more detailed analysis reveals that this is not the case.

The maximum principle for the space and time-space fractional partial differential equations is still an open problem. In this paper, we consider a multi-term time-space Riesz-Caputo fractional differential equations over an open bounded domain. A maximum principle for the equation is proved. The uniqueness and continuous dependence of the solution are derived. Using a fractional predictor-corr...

The Advanced Multilevel Predictor-Corrector Quasi-static Method (AML-PCQM) is proposed in this work. four computational levels, including transport, Multi-Group (MG) Coarse Mesh Finite Difference (CMFD), One-Group (1G) CMFD, and Exact Point-Kinetics Equation (EPKE), are coupled with a new dynamic iteration strategy. In each coupling algorithm, the original Transient Fixed Source Problem (TFSP) ...

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...

We present a generalization of the finite volume evolution Galerkin scheme [17, 18] for hyperbolic systems with spatially varying flux functions. Our goal is to develop a genuinely multi-dimensional numerical scheme for wave propagation problems in a heterogeneous media. We illustrate our methodology for acoustic waves in a heterogeneous medium but the results can be generalized to more complex...

A linear multistep method for solving first order initial value problems of ordinary differential equations is presented in this paper. The approach of collocation approximation is adopted in the derivation of the scheme and then the scheme is applied as simultaneous integrator to first order initial value problems of ordinary differential equations. This implementation strategy is more accurat...

should not be used for the numerical integration of y = /(x, y) if /„ < 0 along the true solution y(x) although the solution of ( 1 ) converges to y(x) for fixed finite x as h —» 0 (see, e.g., [1]). In fact, rapid oscillations, with an amplitude increasing exponentially as the numerical integration proceeds, will supersede the values approximating?/ (x) and eventually destroy the meaningfulness...

The folding and misfolding mechanism of multidomain proteins remains poorly understood. Although thermodynamic instability of the first nucleotide-binding domain (NBD1) of ΔF508 CFTR (cystic fibrosis transmembrane conductance regulator) partly accounts for the mutant channel degradation in the endoplasmic reticulum and is considered as a drug target in cystic fibrosis, the link between NBD1 and...