Corrigendum to: “A new regularized method for two dimensional nonhomogeneous backward heat problem” [Appl. Math. Comput. 215 (2009) 873–880]

2013 ◽  
Vol 219 (9) ◽  
pp. 4931-4932
Author(s):  
Nguyen Huy Tuan
Keyword(s):  
Two Dimensional ◽  
Heat Problem ◽  
Regularized Method ◽  
Appl Math ◽  
Backward Heat Problem

The truncation method for a two-dimensional nonhomogeneous backward heat problem

2010 ◽  
Vol 216 (12) ◽  
pp. 3423-3432 ◽  
Author(s):  
Phan Thanh Nam ◽  
Dang Duc Trong ◽  
Nguyen Huy Tuan
Keyword(s):  
Two Dimensional ◽  
Heat Problem ◽  
Truncation Method ◽  
Backward Heat Problem

scholarly journals Two-Parameter Regularization Method for a Nonlinear Backward Heat Problem with a Conformable Derivative

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Vu Ho ◽  
Donal O’Regan ◽  
Hoa Ngo Van
Keyword(s):  
Integral Equation ◽  
Regularization Method ◽  
Time Variable ◽  
Conformable Derivative ◽  
Heat Problem ◽  
Regularization Parameters ◽  
Ill Posed ◽  
Parameter Regularization ◽  
Two Parameter ◽  
Backward Heat Problem

In this paper, we consider the nonlinear inverse-time heat problem with a conformable derivative concerning the time variable. This problem is severely ill posed. A new method on the modified integral equation based on two regularization parameters is proposed to regularize this problem. Numerical results are presented to illustrate the efficiency of the proposed method.

Interface Cracks in Kirchhoff Anisotropic Thin Plates of Dissimilar Materials

2013 ◽  
Vol 80 (4) ◽  
Author(s):  
Xu Wang ◽  
Peter Schiavone
Keyword(s):  
Thin Plate ◽  
Interfacial Crack ◽  
Dissimilar Materials ◽  
Thin Plates ◽  
Two Dimensional ◽  
Structure And Properties ◽  
Intensity Factors ◽  
Crack Tip Field ◽  
Anisotropic Plates ◽  
Appl Math

This paper investigates the problem of stretching and bending deformations of a Kirchhoff anisotropic thin plate composed of two dissimilar materials bonded along a straight interface containing a crack. Our analysis makes use of the Stroh octet formalism developed recently by Cheng and Reddy (Cheng and Reddy, 2002, “Octet Formalism for Kirchhoff Anisotropic Plates,” Proc. R. Soc. Lond., A458, pp. 1499–1517; Cheng and Reddy, 2003, “Green’s Functions for Infinite and Semi-Infinite Anisotropic Thin Plates,” ASME J. Appl. Mech., 70, pp. 260–267; Cheng and Reddy, 2004, “Laminated Anisotropic Thin Plate With an Elliptic Inhomogeneity,” Mech. Mater., 36, pp. 647–657; Cheng and Reddy, 2005, “Structure and Properties of the Fundamental Elastic Plate Matrix,” J. Appl. Math. Mech., 85, pp. 721–739) for Kirchhoff anisotropic plates. It is found that the interfacial crack-tip field consists of a pair of two-dimensional oscillatory singularities, which are explicitly determined. Two complex intensity factors are proposed to evaluate the two oscillatory singularities.

scholarly journals One- and Multi-dimensional CWENOZ Reconstructions for Implementing Boundary Conditions Without Ghost Cells

2021 ◽  
Author(s):  
M. Semplice ◽  
E. Travaglia ◽  
G. Puppo
Keyword(s):  
Boundary Conditions ◽  
The Novel ◽  
Two Dimensional ◽  
Finite Volume Schemes ◽  
Third Order ◽  
One Dimensional ◽  
Numerical Tests ◽  
Ghost Cells ◽  
The One ◽  
Appl Math

AbstractWe address the issue of point value reconstructions from cell averages in the context of third-order finite volume schemes, focusing in particular on the cells close to the boundaries of the domain. In fact, most techniques in the literature rely on the creation of ghost cells outside the boundary and on some form of extrapolation from the inside that, taking into account the boundary conditions, fills the ghost cells with appropriate values, so that a standard reconstruction can be applied also in the boundary cells. In Naumann et al. (Appl. Math. Comput. 325: 252–270. 10.1016/j.amc.2017.12.041, 2018), motivated by the difficulty of choosing appropriate boundary conditions at the internal nodes of a network, a different technique was explored that avoids the use of ghost cells, but instead employs for the boundary cells a different stencil, biased towards the interior of the domain. In this paper, extending that approach, which does not make use of ghost cells, we propose a more accurate reconstruction for the one-dimensional case and a two-dimensional one for Cartesian grids. In several numerical tests, we compare the novel reconstruction with the standard approach using ghost cells.

scholarly journals Extinction of a two species non-autonomous competitive system with Beddington-DeAngelis functional response and the effect of toxic substances

2016 ◽  
Vol 14 (1) ◽  
pp. 1157-1173 ◽  
Author(s):  
Fengde Chen ◽  
Xiaoxing Chen ◽  
Shouying Huang
Keyword(s):  
Functional Response ◽  
Global Attractivity ◽  
Sufficient Conditions ◽  
The Other ◽  
Toxic Substances ◽  
Two Dimensional ◽  
Competitive System ◽  
Volterra Systems ◽  
Appl Math

AbstractA two species non-autonomous competitive phytoplankton system with Beddington-DeAngelis functional response and the effect of toxic substances is proposed and studied in this paper. Sufficient conditions which guarantee the extinction of a species and global attractivity of the other one are obtained. The results obtained here generalize the main results of Li and Chen [Extinction in two dimensional nonautonomous Lotka-Volterra systems with the effect of toxic substances, Appl. Math. Comput. 182(2006)684-690]. Numeric simulations are carried out to show the feasibility of our results.

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