International Journal of Applied Nonlinear Science (5 papers in press)

Regular Issues

• An SEIR epidemic models global analysis that incorporates the bi-linear incidence rate with treatment function  
  by S.K. Tiwari, Pradeep Porwal, Neha Mangal 
  Abstract: In this paper, the bi-linear incidence rate and saturated treatment function of the SEIR epidemic model are examined, with a particular emphasis on the impact of inadequate treatment on the infectious diseases transmissibility. The basic reproductive number, which determines the potential for disease extinction or persistence, is evaluated. The determination of threshold requirements for all types of equilibrium points is examined. We prove that the equilibrium is locally asymptotically stable by calculating the eigenvalues and using the Routh-Hurwitz criterion. The autonomous convergence theorem and the Lyapunov function are also used to investigate the disease-free and endemic equilibriums global asymptotical stability. The research carried out suggested that the commencement of treatment is a highly relevant element in infection control. The results of the numerical simulations are used to support and verify the theoretical findings.
  Keywords: mathematical models; epidemiology; treatment; basic reproduction number; stability analysis.
  DOI: 10.1504/IJANS.2023.10062875
   
  
• Attractor of generalised countable ultrametrisable iterated function system through Gromov-Hausdorff ultrametric  
  by M. Priya, R. Uthayakumar 
  Abstract: In the disciplines like matching of articulated objects, molecular biology, and face recognition, the advantage of shape acquisition and modelling results in greater attention. An optimal approach to handling these shape matching and recognition issues is Gromov-Hausdorff distance, a technique to identify the similarity between shapes. Noting the major contribution of this special metric, this article shows its interest to derive a fixed point theorem on the complete ultrametric space for a cyclic (-)-contraction. With this new fixed point theorem and a few additional results, this study defines the ideology of a generalised countable ultrametrisable iterated function system, and the description of the generalised Hutchinson-Barnsley operator is provided. Finally, the classical Hutchinson-Barnsley theorem (HB theorem, for short) employed in the newly formulated iterated function system shows the fractal set of the iterated function system (simply IFS).
  Keywords: Gromov-Hausdorff ultrametric space; Gromov-Hausdorff distance; iterated function system; IFS; attractor; fractal; HB theory.
  DOI: 10.1504/IJANS.2024.10064439
   
  
• A novel attractor for an IFS having generalised contractions in dislocated quasi metric space  
  by M. Priya, A.A. Navish, R. Uthayakumar 
  Abstract: Fixed point theory has a wide application in mathematics and this article initially builds a modern fixed point theorem for generalised contractive type functions on a complete dislocated quasi metric space (DQMS, in short). A standard procedure for appraising the attractor of an iterated function system (IFS, simply) is working with fixed point theory and performing the Hutchinson-Baransley theory (in brief, HB theory) and in the perspective of this theorem, an IFS comprising a finite number of generalised contractive mappings is considered. Also, it can be appraised that the parameters of the contraction functions of a fractal image through an IFS and as a consequence of this process, one can synthesise it, calling it an inverse problem. Finally, the conventional HB theory is performed. As a result of this, we picked up an attractor (fractal) as a fixed point of the HB operator.
  Keywords: dislocated quasi metric space; generalised contractive mapping; HB theory; attractor; fractal; iterated function system.
  DOI: 10.1504/IJANS.2024.10064441
   
  
• Modelling solitary wave via numerical solution of Korteweg de Vries and KdV-Burger equation using differential quadrature  
  by Debabrata Datta, Swakantik Mishra, S. Suman Rajest, M. Sakthivanitha, D. Kerana Hanirex, S. Silvia Priscila 
  Abstract: The prime objective of the coastal engineering community is to protect near-shore areas. Because they lessen shock from single waves near coastal locations, artificial structures may protect. A single wave propagates without changing shape or size. The mathematical description of solitary wave explains that the global peak of solitary wave decays gradually far away from the peak. The solitary wave can be obtained by solving the Korteweg de Vries (KdV) equation analytically or numerically and also develops a numerical solver of the KdV equation to understand the behaviour of travelling waves. The research is also extended to develop the numerical solution of the KdV-Burger equation to understand the travelling characteristics of heat waves. Traditional finite difference methods can be applied to have the corresponding numerical solutions. However, in this research, the challenge is to develop numerical solutions of KdV and KdV-Burger equations using an innovative numerical method such as differential quadrature. The basic idea of differential quadrature is to approximate partial derivatives of any order as a matrix. L2 norm and L are computed for stability analysis of the outcome of the differential quadrature method.
  Keywords: KdV equation; KdV-Burger equation; differential quadrature; L2 norm; characteristics of heat waves; physics of solitary wave; mathematical structure; detect stability; finite volume element.
  DOI: 10.1504/IJANS.2024.10064683
   
  
• A new modified Taylor wavelets collocation method for solving convection diffusion and Benjamina Bona Mohany equations  
  by Ankit Kumar, Sag Ram Verma 
  Abstract: In this work, a novel method is presented for solving the convection-diffusion and Benjamina Bona Mohany equations. And these partial differential equations are used for mathematical modelling of semiconductor and optical devices. The introduced method is based on new modified Taylor wavelets approximation which is directly used to convert the equations to a system of algebraic equation by combining collocation method. In this novel method, an improved factor is multiplied in the modified Taylor wavelets basis which further improves the results. Also the effect of the improvement factor and time on solution results of these problems for different domains of z is discussed in this paper. To demonstrate the reliability and stability of this novel method, we compared its results with previously used methods, such as the finite difference method, and Haar wavelet method. Consequently, the proposed method yields a significantly improved approximation solution for various classes of partial differential equations.
  Keywords: Benjamina Bona Mohany equation; convection diffusion equation; collocation points; numerical problems; improvement factor; new modified Taylor wavelets.
  DOI: 10.1504/IJANS.2024.10065175