Registered Data

[CT049]

[01079] Higher order numerical scheme to approximation generalized Caputo fractional derivatives and its application

  • Session Date & Time : 2C (Aug.22, 13:20-15:00)
  • Type : Contributed Talk
  • Abstract : In this paper, a high-order numerical scheme is established to approximate the generalized Caputo fractional derivative using Lagrange interpolation formula. Order of convergence for this scheme is obtained as (4 − α), where α ∈ (0, 1) is the order of generalized Caputo fractional derivative. The local truncation error of the approximation is also obtained. Further, the developed scheme is used to solve the generalized fractional advection-diffusion equation. Stability and convergence are also discussed for the difference scheme. In the last, numerical examples are discussed to illustrate the theoretical results.
  • Classification : 35R11, 26A33, 65R10
  • Author(s) :
    • Sarita kumari (Indian Institute of technology (Banaras Hindu University))
    • Dr. Rajesh Kumar Pandey (Indian Institute of Technology (BHU) Varanasi)

[01551] Observer-based Nonlinear Fault-tolerant Control Design for Fractional-order Parabolic PDE Systems

  • Session Date & Time : 2C (Aug.22, 13:20-15:00)
  • Type : Contributed Talk
  • Abstract : The problem of robust stabilization for fractional-order parabolic PDE systems with nonlinear actuator faults is considered. The main aim of this work is to design an observer-based nonlinear fault-tolerant controller for obtaining the required results. Then, a set of conditions are derived with the aid of Lyapunov-based approach for the stabilization analysis. Further, the theoretical results are verified through the numerical example with graphical results.
  • Classification : 35R11, 93Dxx, 93Cxx, 37Mxx, 37N35
  • Author(s) :
    • Sweetha Senthilrathnam (Bharathiar university)
    • Sakthivel Rathinasamy (Bharathiar University)

[01928] Advanced Computational Methods for Fractional Partial Differential Equations

  • Session Date & Time : 2C (Aug.22, 13:20-15:00)
  • Type : Contributed Talk
  • Abstract : The proposed numerical method comprises the approximation of both integer and non-integer derivatives of the fractional order convection-diffusion-reaction problems by the derivatives of the orthogonal polynomials. Both integer and non-integer derivatives of orthogonal polynomials are represented as the product of matrices. In fact, these types of matrices are known as operational matrices. Finally, with the aid of operational matrices, the fractional differential equation is reduced into a system of linear or nonlinear algebraic equations.
  • Classification : 35R11, 65Mxx, Numerical methods for fractional partial differential equation
  • Author(s) :
    • Ashish Awasthi (National Institute of Technology Calicut)
    • Poojitha S (National Institute of Technology Calicut)

[02638] A note on contribution of finite difference methods for fractional diffusion equations

  • Session Date & Time : 2C (Aug.22, 13:20-15:00)
  • Type : Contributed Talk
  • Abstract : Since the last two decades, extensive research has been carried out on the numerical solution of fractional diffusion equations, particularly in finite difference methods. The finite difference schemes play a crucial role in obtaining the solution of fractional diffusion equations. The most popular are the explicit finite difference method, implicit finite difference method, and Crank-Nicolson finite difference method. This article focuses on developing finite difference schemes for fractional diffusion equations. Also, the stability and convergence of finite difference methods will be discussed by using the matrix norm method. Moreover, it will compare methods in the sense of accuracy and rate of convergence of these schemes. The last section will be devoted to the test problems.
  • Classification : 35R11, 65M06, 65M12
  • Author(s) :
    • GUNVANT ACHUTRAO BIRAJDAR (Tata Institute of Social Sciences Tuljapur Campus)

[00875] Deep learning based reduced ensemble Kalman inversion for microscopic parameter estimation

  • Session Date & Time : 2C (Aug.22, 13:20-15:00)
  • Type : Contributed Talk
  • Abstract : In the scope of nonlinear multiscale problems, estimating the macroscopic distribution of the microscopic geometrical parameters given macroscopic measurements is of interest. In general, inverse estimation is challenging due to the need of derivatives of the complex forward model and the high cost of the forward solver. We introduce derivative-free ensemble Kalman inversion and deep-learning based model reduction to tackle the aforementioned challenges, and assess the performance of the proposed method on a hyper-elastic problem.
  • Classification : 35R30, 65N21, 74G75, 65N75, 62F86
  • Author(s) :
    • Yankun Hong (Eindhoven University of Technology)
    • Harshit Bansal (Eindhoven University of Technology)
    • Karen Veroy (Eindhoven University of Technology)