Article
Acoustics
Qamar Din, Waqas Ishaque, Muhammad Asad Iqbal, Umer Saeed
Summary: A modification to the classical Nicholson-Bailey model is proposed in this article, with the addition of a safe refuge assumption for hosts from parasitoid attacks. It is found that the modified model exhibits stable coexistence under this assumption, and Neimark-Sacker bifurcation at positive steady-state is interrogated using normal forms theory. Chaos control methods are implemented to escape bifurcating and chaotic behavior, with numerical simulations used for illustration and real observed field data included to support the theoretical discussion.
JOURNAL OF VIBRATION AND CONTROL
(2022)
Article
Mathematics, Applied
Reetika Chawla, Komal Deswal, Devendra Kumar, Dumitru Baleanu
Summary: This paper presents a new approach to investigate the time-fractional advection-dispersion equation extensively used in studying transport processes. A new modified fractional derivative operator, based on Atangana-Baleanu's definition of a derivative in the Caputo sense, is proposed, involving singular and non-local kernels. A numerical approximation of this new operator is provided and applied to an advection-dispersion equation. Through Fourier analysis, it is proved that the proposed scheme is unconditionally stable. Numerical examples validate the theoretical results and demonstrate the proficiency of the numerical scheme.
Article
Engineering, Mechanical
Yuying Liu, Junjie Wei
Summary: This paper investigates a delayed Nicholson equation with delay harvesting term proposed as open problems and conjectures. Stability switching curves are obtained by taking two delays as parameters using a method introduced by An et al. The existence of Hopf singularity on a two-parameter plane is determined by the varying direction of two parameters, and the normal form near the Hopf singularity is derived through the application of center manifolds theory and normal forms method of FDEs. Finally, numerical simulations are conducted to illustrate the theoretical conclusions.
NONLINEAR DYNAMICS
(2021)
Article
Computer Science, Interdisciplinary Applications
Yajun An
Summary: This paper presents a unified methodology for deriving dispersion reduction FD schemes for the two-dimensional acoustic wave equation, which aims to reduce dispersion issues while ensuring the theoretical minimum dispersion error. The stability criteria for the general scheme are discussed, and the equivalence between popular dispersion reduction methodologies and theoretical numerical reduction methodologies is emphasized.
JOURNAL OF COMPUTATIONAL PHYSICS
(2021)
Article
Mathematics, Applied
Hatef Dastour, Wenyuan Liao
Summary: This paper presents a general approach for constructing fourth-order finite difference schemes for the Helmholtz equation with PML and successfully develops two optimal fourth-order finite difference schemes. By implementing a refined choice strategy for selecting optimal parameters, the new methods demonstrate accuracy and effectiveness in reducing numerical dispersion.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2021)
Article
Geochemistry & Geophysics
Rune Mittet
Summary: There are numerical accuracy issues related to implementing sharp internal interfaces in pseudospectral and finite-difference schemes. Numerical errors due to interface implementation can be classified based on Taylor or Fourier expansion orders. Pseudospectral method does not provide spectral accuracy in inhomogeneous media, and aliasing effects can affect the numerical errors of propagating fields. High-order finite differences can achieve the same accuracy as pseudospectral method, and smoothing of material-parameter fields can further reduce error-free bandwidth.
Article
Mathematics, Interdisciplinary Applications
Dauda Gulibur Yakubu, Abdulhameed Mohammed, Adamu Garba Tahiru, Kadas Saidu Abubakar, Magaji Yunbunga Adamu
Summary: Mathematical models and numerical simulations are used to understand and predict the development and treatment of cancer, particularly breast cancer. Current treatments have limitations and there is a need to focus on prevention and finding more effective treatment methods.
FRACTAL AND FRACTIONAL
(2023)
Article
Mathematics, Applied
Tingting Wu, Yuran Sun, Dongsheng Cheng
Summary: A new finite difference scheme for 3D Helmholtz problem with compact and fourth-order accuracy is proposed in this paper. By minimizing numerical dispersion, the efficiency of the new scheme is demonstrated. Additionally, a Bi-CGSTAB iterative solver is developed for solving sparse and large linear systems, leading to improved computational efficiency.
APPLIED NUMERICAL MATHEMATICS
(2021)
Article
Mathematics, Applied
Theodoros T. Zygiridis, Stamatios A. Amanatiadis, Aristeides D. Papadopoulos, Nikolaos Kantartzis
Summary: This work presents a finite-difference time-domain (FDTD) methodology that allows for controllable accuracy within prescribed frequency bands, dealing with material dispersion described by the Lorentz model. An optimization technique based on the one-dimensional numerical dispersion relation is introduced to modify the form of the spatial operators, ensuring that the numerical wavenumber closely matches the exact one in specific frequency ranges.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2023)
Article
Multidisciplinary Sciences
Mir Aijaz, Ibrahim M. Almanjahie, Javid Gani Dar
Summary: The paper examines the change in fluid distribution in human skin when immersed in water of different temperatures and discusses the effects of water immersion on impaired vascular function and muscle soreness during physiotherapy treatments.
JOURNAL OF ADVANCED RESEARCH
(2021)
Article
Mathematics, Applied
Lizhuang Huang, Zhiting Xu
Summary: In this paper, a diffusive Nicholson's Blowflies equation with two delays is considered, and a new upper solution for the wave equation is constructed. The existence of traveling wave fronts connecting the two equilibria is shown, and the non-existence of traveling waves of the equation is obtained. This paper can serve as a corrigendum for the paper by Huang and Liu (2022).
APPLIED MATHEMATICS LETTERS
(2023)
Article
Environmental Sciences
Liang Chen, Jianping Huang, Li-Yun Fu, Weiting Peng, Cheng Song, Jiale Han
Summary: This study presents an optimized tridiagonal compact finite difference (CFD) scheme for spatial and temporal derivatives approximation in seismic wave equation simulation. Experimental results show that the optimized CFD scheme is more accurate than the regular CFD scheme in certain wavenumber ranges. Furthermore, the accuracy of the optimized CFD scheme is examined in wavefield modeling of complex structures using a Marmousi model, and the results demonstrate that the optimized CFD4 scheme provides a more accurate wavefield than the regular CFD4 scheme when the upper limit of the integral function is 0.5 pi and 0.75 pi.
Article
Mathematics, Applied
Pierre-Henri Cocquet, Martin J. Gander, Xueshuang Xiang
Summary: A new finite difference scheme is proposed for dispersion correction in solving the two-dimensional Helmholtz equation in rectangular domains, which proves to be sixth order accurate for plane wave solutions. Numerical experiments demonstrate minimal dispersion error with few points per wavelength, making the scheme effective for solving Helmholtz problems using multigrid.
SIAM JOURNAL ON SCIENTIFIC COMPUTING
(2021)
Article
Engineering, Mechanical
Syed Abbas, Michal Niezabitowski, Said R. Grace
Summary: A generalized Nicholson blowflies model with harvesting or immigration and random effect is studied, and the existence of positive global solution and estimate on Lyapunov exponent are discussed. Nontrivial equilibrium solution is proven to be mean square exponential stability and stable in probability. The importance of noise in all qualitative properties of the solution is emphasized, and numerical simulations validate the analytical findings, which contribute to the existing literature.
NONLINEAR DYNAMICS
(2021)
Article
Mathematics, Applied
Hatef Dastour, Wenyuan Liao
Summary: This paper presents an optimal 13-point finite difference scheme for the Helmholtz equation with a PML in the two-dimensional domain, aiming to minimize numerical dispersion through error analysis, and provides two practical strategies for selecting optimal parameters. Several numerical examples are solved to demonstrate the accuracy and effectiveness of the new method in reducing numerical dispersion.
NUMERICAL ALGORITHMS
(2021)
Article
Fisheries
Wanna Sirimanapong, Alexandra Adams, Ei Lin Ooi, Darren M. Green, Dang Khoa Nguyen, Craig L. Browdy, Bertrand Collet, Kim D. Thompson
FISH & SHELLFISH IMMUNOLOGY
(2015)
Article
Fisheries
Wanna Sirimanapong, Kim D. Thompson, Ei Lin Ooi, Michael Bekaert, Bertrand Collet, John B. Taggart, James E. Bron, Darren M. Green, Andrew P. Shinn, Alexandra Adams, Michael J. Leaver
FISH & SHELLFISH IMMUNOLOGY
(2015)
Article
Fisheries
Greta Carmona-Antonanzas, Joseph L. Humble, Stephen N. Carmichael, Jan Heumann, Hayden R. L. Christie, Darren M. Green, David I. Bassett, James E. Bron, Armin Sturm
Article
Biochemical Research Methods
Tom Sumner, Richard J. Orton, Darren M. Green, Rowland R. Kao, Simon Gubbins
PLOS COMPUTATIONAL BIOLOGY
(2017)
Article
Infectious Diseases
R. J. Orton, M. Deason, P. R. Bessell, D. M. Green, R. R. Kao, L. C. M. Salvador
Article
Fisheries
Silvia Soares, Alexander G. Murray, Mags Crumlish, James F. Turnbull, Darren M. Green
Article
Fisheries
M. Werkman, A. G. Murray, L. A. Munro, J. F. Turnbull, D. M. Green
Article
Fisheries
Silvia Soares, Alexander G. Murray, Mags Crumlish, James F. Turnbull, Darren M. Green
DISEASES OF AQUATIC ORGANISMS
(2013)
Article
Engineering, Environmental
Patrik John Gustav Henriksson, Jeroen Bartholomeus Guinee, Reinout Heijungs, Arjan de Koning, Darren Michael Green
INTERNATIONAL JOURNAL OF LIFE CYCLE ASSESSMENT
(2014)
Article
Fisheries
D. M. Green, M. Werkman, L. A. Munro
JOURNAL OF FISH DISEASES
(2012)
Article
Fisheries
B. Oidtmann, S. E. LaPatra, D. Verner-Jeffreys, M. Pond, E. J. Peeler, P. A. Noguera, D. W. Bruno, S. St-Hilaire, C. B. Schubiger, K. Snekvik, M. Crumlish, D. M. Green, M. Metselaar, H. Rodger, H. Schmidt-Posthaus, M. Galeotti, S. W. Feist
JOURNAL OF FISH DISEASES
(2013)
Article
Biology
Michael Taylor, Peter L. Simon, Darren M. Green, Thomas House, Istvan Z. Kiss
JOURNAL OF MATHEMATICAL BIOLOGY
(2012)
Article
Multidisciplinary Sciences
Darren M. Green, David J. Penman, Herve Migaud, James E. Bron, John B. Taggart, Brendan J. McAndrew
Article
Infectious Diseases
A. E. Jones, L. A. Munro, D. M. Greed, K. L. Morgan, A. G. Murray, R. Norman, D. Ryder, N. K. G. Salama, N. G. H. Taylor, M. A. Thrush, I. S. Wallace, K. J. Sharkey
Article
Infectious Diseases
Nattakan Saleetid, Darren Michael Green
TRANSBOUNDARY AND EMERGING DISEASES
(2019)