Registered Data

[CT017]

  • Session Time & Room
    • CT017 (1/1) : 3D @G402 [Chair: Yogita Mahesh Mahatekar]
  • Classification
    • CT017 (1/1) : General theory for ordinary differential equations (34A) / Asymptotic theory for ordinary differential equations (34E) / Functions of one variable (26A)

[01974] Solving fractional Hantavirus model: A new approach

  • Session Time & Room : 3D (Aug.23, 15:30-17:10) @G402
  • Type : Contributed Talk
  • Abstract : In the present work, fractional order Hantavirus epidemic model introduced by \cite{peixoto2006effect,hantavirus2010modeling} is integrated using new iterative method (NIM) and implicit $\theta-$ method ($\theta=1$). New iterative method has been developed by Daftardar-Gejji and H. Jafari \cite{daftardar2006iterative}. Using new iterative method and $ \theta-$ method \cite{yakit2018explicit}, we have developed a new numerical algorithm to solve fractional differential equations (FDEs) in the Hantavirus model. Dynamics of the hanta virus model is studied. Hantavirus model of fractional order represents mouse population before and after getting influenced by Hantavirus under various conditions and its effect on birth rate and death rate of mice is studied. This model represents a Hantavirus infection in rodents and alien population. It has been observed that solution obtained by new algorithm is accurate and in good agreement when compared with solution obtained by other established algorithms. Further, effects of harvesting efforts $E(t)$ as an optimal control on spread of Hantavirus infection is studied. It has been observed that, population of both susceptible and infected rodents minimizes when we apply optimal control.
  • Classification : 34AXX, 03-XX, 26AXX
  • Format : Talk at Waseda University
  • Author(s) :
    • Yogita Mahesh Mahatekar (COEP Technological University)
    • Amey Deshpande (MIT World peace University)

[01748] Large-scale mRNA translation and the intricate effects of competition for the finite pool of ribosomes

  • Session Time & Room : 3D (Aug.23, 15:30-17:10) @G402
  • Type : Contributed Talk
  • Abstract : We develop a mathematical network model based on balance non-linear first order ordinary differential equations to study large-scale simultaneous mRNA translation in the cell. The central feature of the model is that it is a cooperative system and this property guarantees the monotonicity of the flow. We derive that trajectories within each level set of the first integral globally converge to the fixed point. One of our findings is that raising the drop-off rate in an mRNA that is "jammed" by ribosomes can increase the network's overall protein synthesis rate.
  • Classification : 34E10, 37N25, 92-10, 93D20
  • Format : Talk at Waseda University
  • Author(s) :
    • Aditi Jain (IIT Ropar)
    • Michael Margaliot (Tel Aviv University)
    • Arvind Kumar Gupta (IIT Ropar)

[01668] Order Reconstruction in Microfluidic Channels

  • Session Time & Room : 3D (Aug.23, 15:30-17:10) @G402
  • Type : Contributed Talk
  • Abstract : We analytically and numerically study Order reconstruction (OR) solutions within the Landau-de Gennes theory for nematic liquid crystals in long shallow channel geometries. OR solutions describe liquid crystal polydomains, i.e., subdomains of distinct director orientation separated by domain walls. Such solutions are of interest due to their potential applications in drug delivery technologies and optical devices for instance. We investigate OR solutions in different physical settings: nematic liquid crystals, passive and active nematodynamics, and ferronematics.
  • Classification : 34E10, 76A15, 34A99
  • Format : Online Talk on Zoom
  • Author(s) :
    • James Dalby (University of Strathclyde)

[02390] Discontinuous Galerkin method for time-fractional delay differential equation

  • Session Time & Room : 3D (Aug.23, 15:30-17:10) @G402
  • Type : Contributed Talk
  • Abstract : In this article, we analyze the discontinuous Galerkin method for time-fractional partial differential equation with delay term $u(\theta(t))$, where $\theta(t)=t-\tau(t)< t$. The well-posedness of the fully discrete scheme for a fractional delay system is investigated. Also, we show the optimal order of convergence in the energy norm. Some numerical results are provided to support theoretical results.
  • Classification : 26A33, 35D30, 65M60, 34K37
  • Format : Talk at Waseda University
  • Author(s) :
    • Raksha Devi (Department of Mathematics, Indian Institute of Technology, Roorkee )
    • Dwijendra N. Pandey (Department of Mathematics, Indian Institute of Technology, Roorkee )

[01090] A high order approximation scheme for non-linear time fractional reaction-diffusion equation

  • Session Time & Room : 3D (Aug.23, 15:30-17:10) @G402
  • Type : Contributed Talk
  • Abstract : We discuss a high order numerical scheme for the non-linear time fractional reaction-diffusion equation of order $\alpha\in (0, 1)$. A cubic approximation and compact finite difference schemes are used to approximate the time-fractional and spatial derivatives respectively. The numerical scheme achieves convergence rate of order $4-\alpha$ in the temporal direction and $4$ in the spatial direction. Further, numerical experimentation is performed to demonstrate the authenticity of the proposed numerical scheme.
  • Classification : 26A33, 35R11, 35A35
  • Format : Online Talk on Zoom
  • Author(s) :
    • Rajesh Kumar Pandey (Indian Institute of Technology (BHU) Varanasi)
    • Deeksha Singh (Indian Institute of Technology (BHU) Varanasi)