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128 results on '"Long, Guangqing"'

11. Numerical Solution of Singularly Perturbed Convection Delay Problems Using Self-adaptive Differential Evolution Algorithm

Author

Long, Guangqing, Liu, Li-Bin, Huang, Zaitang, Hutchison, David, Series Editor, Kanade, Takeo, Series Editor, Kittler, Josef, Series Editor, Kleinberg, Jon M., Series Editor, Mattern, Friedemann, Series Editor, Mitchell, John C., Series Editor, Naor, Moni, Series Editor, Pandu Rangan, C., Series Editor, Steffen, Bernhard, Series Editor, Terzopoulos, Demetri, Series Editor, Tygar, Doug, Series Editor, Weikum, Gerhard, Series Editor, Huang, De-Shuang, editor, Gromiha, M. Michael, editor, Han, Kyungsook, editor, and Hussain, Abir, editor

Published
2018
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40. Numerical analysis of a system of semilinear singularly perturbed first‐order differential equations on an adaptive grid.

Author

Liu, Li‐Bin, Zhu, Ciwen, and Long, Guangqing

Subjects
DIFFERENTIAL equations, NUMERICAL analysis, INITIAL value problems, ENZYME kinetics, NONLINEAR systems, DELAY differential equations
Abstract

An adaptive grid method based on the backward Euler formula for a system of semilinear singularly perturbed initial value problems is studied. Based on the a priori error analysis and mesh equidistribution principle, we prove that the convergence rate of our semidiscrete adaptive grid method is first order, which is robust with respect to the perturbation parameters. Then, in order to construct a fully discrete adaptive grid method, a standard residual‐type a posterior error estimation is constructed by using the linear polynomial interpolation technique. A partly heuristic argument based on this a posteriori error estimator leads to an optimal monitor function, which is used to design an adaptive grid algorithm. Furthermore, we also extend our presented adaptive grid method to a nonlinear system of singularly perturbed problem arising in the modeling of enzyme kinetics and a system of singularly perturbed delay differential equations, respectively. Finally, numerical results are provided to illustrate the effectiveness of our presented adaptive grid method. [ABSTRACT FROM AUTHOR]

Published
2022
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49. Discrete Legendre spectral Galerkin method for Urysohn integral equations.

Author

Das, Payel, Nelakanti, Gnaneshwar, and Long, Guangqing

Subjects
GALERKIN methods, LEGENDRE'S functions, INTEGRAL equations, KERNEL functions, STOCHASTIC convergence
Abstract

In this paper, we consider the discrete Legendre spectral Galerkin method to approximate the solution of Urysohn integral equation with smooth kernel. The convergence of the approximate and iterated approximate solutions to the actual solution is discussed and the rates of convergence are obtained. In particular we have shown that, when the quadrature rule is of certain degree of precision, the superconvergence rates for the iterated Legendre spectral Galerkin method are maintained in the discrete case. [ABSTRACT FROM PUBLISHER]

Published
2018
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