Abstract: Publication date: 1 June 2019Source: Applied Mathematics and Computation, Volume 350Author(s): Zülfigar Akdoğan, Ali Yakar, Mustafa Demirci The main purpose of this study is the investigation of discontinuous Sturm–Liouville problem with fractional derivatives. We give an operator theoretic framework of the problem under consideration. Namely, we define an operator A in the Hilbert space L2[−1,1], the eigenvalues and corresponding eigenfunctions of which coincide with the eigenvalues and corresponding eigenfunctions of the boundary value problem, respectively. Then, we establish the characteristic function and prove that the eigenvalues of the considered problem coincide with the roots of this characteristic function.

Abstract: Publication date: Available online 11 January 2019Source: Applied Mathematics and ComputationAuthor(s): Peng Lu As one of the typical collective actions or cooperative behaviors of human beings, the rumor is widespread and harmful in the society for most cases. Modeling and predicting the dynamics and evolutions or rumors’ spreading has been widely investigated in existing models, including the (expanded) SIR models. In this paper, a micro-model of neighborhood interactions between agents (ABM) is proposed to explore the mechanism of rumors’ spreading. In the proposed model, the agents (sources or receptors) interact with the neighbors on a square lattice, and the source spreads rumors to receptors, and if the receptors decide to spread rumors they become sources as well. For each agent, the individual judgment heterogeneity and social trust heterogeneity are introduced, and the distance to the original source provides the basic field function. Distance, judgment, and trust consist of the thresholds that should be overcome before the rumor can be spread by certain agent to others. The heard time records the frequency that the rumor is heard, and the agent spreads the rumor if the heard time satisfies the threshold condition. As the mean effects of individual judgment and social trust on rumors’ spreading are stabilized, this paper focuses on their heterogeneity effects. The spreading curves monitors the instant spreading percentage and they have two stages, which are the “rapidly increase stage” with the linear relationship and “slowly increase stage” with the nonlinear relationship. Simulation outcome indicate that heterogeneity promotes the spreading while the homogeneity dampens it. Besides, the conditional effects of social trust heterogeneity under individual judgment heterogeneity coincide with the general effects. This work paves the way for the full-process prediction of rumors’ spreading.

Abstract: Publication date: 15 May 2019Source: Applied Mathematics and Computation, Volume 349Author(s): Mei Wang, Feifei Du, Churong Chen, Baoguo Jia Asymptotic stability of linear nabla Riemann–Liouville (q, h)-fractional difference equation is investigated in this paper. A Liapunov functional is constructed for the fractional difference equation. The sufficient condition for the asymptotic stability of considered equations is proposed. The results are illustrated with the corresponding numerical examples.

Abstract: Publication date: 15 May 2019Source: Applied Mathematics and Computation, Volume 349Author(s): Na An, Chaobao Huang, Xijun Yu Based on the finite difference scheme in temporal and the direct discontinuous Galerkin (DDG) method in spatial, a fully discrete DDG scheme is first proposed to solve the two-dimensional fractional diffusion-wave equation with Caputo derivative of order 1

Abstract: Publication date: 15 May 2019Source: Applied Mathematics and Computation, Volume 349Author(s): Mohsen Rabbani, Reza Arab, Bipan Hazarika The aim of this article is to prove the existence of solution for nonlinear quadratic integral equations using the generalized form of Darbo fixed point theorem with the help of measure of noncompactness and simulation type condensing operator in the Banach space L2[0, 1]. To illustrate validity of the analytical results, we present a nonlinear integral equation as an application. Finally, we introduce an iteration algorithm by modified homotopy perturbation and Adomian decomposition method to find solution of the above problem with a high accuracy.

Abstract: Publication date: 15 May 2019Source: Applied Mathematics and Computation, Volume 349Author(s): Dilek Erkmen, Alexander E. Labovsky An algorithm for resolving magnetohydrodynamic (MHD) flows has been presented recently, that allows for a stable decoupling of the system and uses the penalty-projection method for extra efficiency. The algorithm relies on the choice of Scott–Vogelius finite elements to complement the grad-div stabilization. We propose a small modification of the algorithm, which allows for its usage even with the less sophisticated (and more computationally attractive) Taylor-Hood pair of finite element spaces. We demonstrate numerically, that the new modification of the method is first order accurate in time (as expected by the theory), while the existing method would fail on the Taylor–Hood finite elements (the blow-up of the solution is demonstrated).

Abstract: Publication date: 15 May 2019Source: Applied Mathematics and Computation, Volume 349Author(s): D.S. Rodrigues, P.F.A. Mancera, T. Carvalho, L.F. Gonçalves Immunotherapy is currently regarded as the most promising treatment to fight against cancer. This is particularly true in the treatment of chronic lymphocytic leukemia, an indolent neoplastic disease of B-lymphocytes which eventually causes the immune system’s failure. In this and other areas of cancer research, mathematical modeling is pointed out as a prominent tool to analyze theoretical and practical issues. Its lack in studies of chemoimmunotherapy of chronic lymphocytic leukemia is what motivated us to come up with a simple ordinary differential equation model. It is based on ideas of de Pillis and Radunskaya and on standard pharmacokinetics-pharmacodynamics assumptions. In order to check the positivity of the state variables, we first establish an invariant region where these time-dependent variables remain positive. Afterwards, the action of the immune system, as well as the chemoimmunotherapeutic role in promoting cancer cure are investigated by means of numerical simulations and the classical linear stability analysis. The role of adoptive cellular immunotherapy is also addressed. Our overall conclusion is that chemoimmunotherapeutic protocols can be effective in treating chronic lymphocytic leukemia provided that chemotherapy is not a limiting factor to the immunotherapy efficacy.

Abstract: Publication date: 15 May 2019Source: Applied Mathematics and Computation, Volume 349Author(s): Zhishuang Wang, Quantong Guo, Shiwen Sun, Chengyi Xia The epidemic diseases have been threatening to human health, and it is of high importance to understand the properties of epidemic propagation among the population will help us to take some effective measures to prevent and control epidemic spreading. In this paper, we propose a novel epidemic model by using two-layer multiplex networks to investigate the multiple influence between awareness diffusion and epidemic propagation, where the upper layer represents the awareness diffusion regarding epidemics and the lower layer expresses the epidemic propagation. In the process of awareness diffusion, the unaware individuals will be aware of the epidemics if the ratio between their awareness neighbors and their degrees reaches the specified ratio. For the epidemic spreading in the lower layer, we use the classical SIR(susceptible-infected-recovered) model. We derive the epidemic threshold by using Micro-Markov chain approach. The analytical results indicate that the epidemic threshold is correlated with the awareness diffusion as well as the topology of epidemic networks. Finally, the simulation results further demonstrate the properties of epidemic propagation and validate the analytical results.

Abstract: Publication date: 15 May 2019Source: Applied Mathematics and Computation, Volume 349Author(s): Wenying Zhao, Yuechao Ma, Aihong Chen, Lei Fu, Yutong Zhang This paper discusses the robust optimization by a sliding mode control (SMC) approach for uncertain singular Markovian jump (SMJ) time-varying delay system with nonlinear perturbation, which uncertainties occur randomly. Firstly, a different integral-type sliding mode surface (SMS) and a different Lyapunov–Krasovskii function are introduced. Secondly, by using linear matrix inequalities, sufficient conditions are proposed to ensure the mean-square exponentially admissible (MSEA) with an H∞ performance level γ of the unforced uncertain SMJ time-varying delay system in the specified SMS. Next, a composed SMC law with the parameter uncertainties occurring randomly can ensure the reachability of the predefined SMS. Finally, three numerical examples are given to test the feasibility of the theory.

Abstract: Publication date: 15 May 2019Source: Applied Mathematics and Computation, Volume 349Author(s): Jalal Eddine Bahbouhi, Najem Moussa So far, research into pubic goods games has been limited to studying the effects of leadership in an experimental works. The results found differ according to the population studied, the number of participants and the country chosen, which makes ideas imprecise when it comes to understanding how cooperation evolves. In this article we try to generalize these works by introducing an agent-based model to simulate interactions in public goods games on a graph, and study the impact of leadership by example on the evolution of cooperation among selfish individuals in a scale-free network. Consistent with recent experimental studies, our results show that leading by example leads to a significant increase in the overall contribution and the group’s welfare, as compared to the situation without leadership. We have demonstrated also that strong leaders have an important role in promoting optimal cooperation in public goods games and consequently they bring more welfare to their groups.

Abstract: Publication date: 15 May 2019Source: Applied Mathematics and Computation, Volume 349Author(s): N. Anggriani, H. Tasman, M.Z. Ndii, A.K. Supriatna, E. Soewono, E Siregar Dengue is worldwide problem with around 390 million cases annually. Dengue is caused by four dengue serotypes: DEN1, DEN2, DEN3, DEN4. Individuals obtain lifelong immunity to the serotype they are infected with. This becomes the main underlying assumptions of most modeling work on dengue. However, data from West Java, Indonesia, showed that there is a possibility for individuals to be reinfected by the same strain, which may result in significantly different dengue transmission dynamics. In this paper, we develop a novel multi-strain dengue model taking into account the reinfection with the same dengue serotype. We examine the effects of reinfection with the same serotype, study symmetric epidemiological characteristics and investigate the effects of antibody-dependent enhancement on dengue transmission dynamics by using a mathematical model. We analyse the stability of the model and perform global sensitivity analysis to determine the most influential parameters. We found that the model has four equilibrium points: disease-free, two partially endemic and coexistence equilibria. We also presented two Basic Reproductive Ratio Ri associated with the first and the second strain of the viruses. The stability of the model is determined by the condition of basic reproductive ratio. We found that when the degree of immunity to the same strain, κ, is between zero and one, the existence of endemic equilibrium is determined by κℜi, where ℜi is the basic reproductive ratio. Furthermore, we found that reinfection with the same serotype contributes an increase in the number of primary and secondary dengue cases. The results suggest that it is likely that reinfection with the same serotype may be one of the underlying factors causing an increase in the number of secondary infection.

Abstract: Publication date: 15 May 2019Source: Applied Mathematics and Computation, Volume 349Author(s): Dilek Erkmen, Alexander E. Labovsky An algorithm for resolving magnetohydrodynamic (MHD) flows has been presented recently, that allows for a stable decoupling of the system and uses the penalty-projection method for extra efficiency. The algorithm relies on the choice of Scott–Vogelius finite elements to complement the grad-div stabilization. We propose a small modification of the algorithm, which allows for its usage even with the less sophisticated (and more computationally attractive) Taylor–Hood pair of finite element spaces. We demonstrate numerically, that the new modification of the method is first order accurate in time (as expected by the theory), while the existing method would fail on the Taylor–Hood finite elements (the blow-up of the solution is demonstrated).

Abstract: Publication date: 15 May 2019Source: Applied Mathematics and Computation, Volume 349Author(s): Chao Wang, Zhengjia Sun, Jintao Cui In this paper, we study a new numerical approach for a quad-curl model problem which arises in the inverse electromagnetic scattering problems and magnetohydrodynamics (MHD). We first split the quad-curl problem with homogeneous boundary conditions into a system of second order equations, and then apply a mixed finite element method to solve the resulting system. The perturbed mixed finite element method is constructed by using edge elements. The well posedness of the numerical scheme is derived. The optimal error estimates in H(curl) and L2 norms for the primal and auxiliary variables are obtained, respectively. The theoretical results are verified by numerical experiments.

Abstract: Publication date: 15 May 2019Source: Applied Mathematics and Computation, Volume 349Author(s): Matthew A. Beauregard A numerical approximation is developed, analyzed, and investigated for quenching solutions to a degenerate Kawarada problem with a left and right Riemann-Liouville fractional Laplacian over a finite one dimensional domain. The numerical analysis provides criterion for the numerical approximations to be monotonic, nonnegative, and linearly stable throughout the computation. The numerical algorithm is used to develop an experimental scaling law relating the critical quenching domain size to the order of fractional derivative. Additional experiments indicate that imbalanced left and right derivative transport coefficients can attenuate or prevent quenching from occurring.

Abstract: Publication date: 15 May 2019Source: Applied Mathematics and Computation, Volume 349Author(s): Yong Liu, Chuanqing Gu The shift and invert Arnoldi (SIA) method is a numerical algorithm for approximating the product of Toeplitz matrix exponential with a vector. In this paper, we extend the SIA method to chemical master equation (CME) and propose a SIA algorithm based on the strategy of reorthogonalization (SIRA). We establish a theoretical error of the resulting approximation of SIRA algorithm. Numerical experiments show that the SIRA algorithm is more efficient than the Krylov FSP algorithm in terms of finite models, and the error estimate can be used to determine whether this result obtained by SIRA algorithm is acceptable or not.

Abstract: Publication date: 15 May 2019Source: Applied Mathematics and Computation, Volume 349Author(s): Bingjun Wang, Mingxia Yuan In this paper, we study the solution of coupled forward-backward stochastic differential equation driven by G-Brownian motion with monotone coefficients. Besides, we prove that the solution is the minimal one.

Abstract: Publication date: Available online 19 December 2018Source: Applied Mathematics and ComputationAuthor(s): S.M. Aydoğan, F.M. Sakar Let consider Ap denoting a class of analytical functions defined as f(z)=zp+ap+1zp+1+⋯+ap+nzp+n+⋯ and p-valent in unit disc U={z z

Abstract: Publication date: Available online 1 February 2018Source: Applied Mathematics and ComputationAuthor(s): E. Karimi-Sibaki, A. Kharicha, M. Wu, A. Ludwig, J. Bohacek Electrically resistive CaF2-based slags are extensively used in many metallurgical processes such as electroslag remelting (ESR). Chemical and electrochemical reactions as well as transport of ions in the molten slag (electrolyte) are critical phenomena for those processes. In this paper, an electrochemical system including two parallel, planar electrodes and a completely dissociated electrolyte operating under a DC voltage is modeled. The transport of ions by electro-migration and diffusion is modeled by solving the Poisson–Nernst–Planck (PNP) equations using the Finite Volume Method (FVM). The non-linear Butler–Volmer equations are implemented to describe the boundary condition for the reacting ions at the electrode–electrolyte interface. Firstly, we study a binary symmetrical electrolyte, which was previously addressed by Bazant et al. (2005), to verify the numerical model. Secondly, we employed the model to investigate our target CaF2–FeO system. The electrolyte is consisted of reacting (Fe2+) and non-reacting (Ca+2, O2−, F−) ions. Spatial distributions of concentrations of ions, charge density, and electric potential across the electrolyte at steady state are analyzed. It is found that the Faradaic reaction of the ferrous ion (Fe2+) has negligible impact on the electric potential field at very low current density (