Registered Data

[CT091]

  • Session Time & Room
    • CT091 (1/1) : 4E @E506 [Chair: Sonia -]
  • Classification
    • CT091 (1/1) : Nonlinear algebraic or transcendental equations (65H) / Probabilistic methods, stochastic differential equations (65C) / Hyperbolic equations and hyperbolic systems (35L)

[00668] Solution of Non-linear Problems Through Variant of Newton’s Method with Applications in Engineering

  • Session Time & Room : 4E (Aug.24, 17:40-19:20) @E506
  • Type : Contributed Talk
  • Abstract : Various non-linear problems that formulated from sciences and engineering like Combustion problems, Chemistry of rainwater, Heat problems, etc. are difficult to solve with analytical methods. So, the approximate solution of such non-linear problems is obtained through iterative methods. Hence, we will discuss variant of Newton’s method and its validity in terms of a convergence order, minimum computation cost, time, and efficiency over existing techniques.
  • Classification : 65H10, 41A58, 65Y20, Numerical Analysis
  • Format : Talk at Waseda University
  • Author(s) :
    • Sonia Bhalla (Chandigarh University)

[01309] Deep Learning Methods for BSDEs/PDEs in Finance

  • Session Time & Room : 4E (Aug.24, 17:40-19:20) @E506
  • Type : Contributed Talk
  • Abstract : In this work we present both a multistep deep learning method with automatic differentiation for the resolution of nonlinear PDEs and BSDEs and an adaptation of the Deep BSDE method for Quadratic BSDE and HJB equations. An approximation error result and error rate is proved for the schemes when using a class of networks with sparse weights. Applications to finance including CVA, portfolio optimisation under exponential utility and options pricing will be presented.
  • Classification : 65Cxx, 65Nxx, 60Hxx, 91Gxx, 68T07
  • Format : Talk at Waseda University
  • Author(s) :
    • Daniel Bussell (UCL)

[00008] Semi Analytic Solution for Coupled (n+1)-dimensional Viscous Burgers' Equation using Homotopy Perturbation Method

  • Session Time & Room : 4E (Aug.24, 17:40-19:20) @E506
  • Type : Contributed Talk
  • Abstract : Semi analytic solution for coupled (n+1)-dimensional non-linear viscous Burgers' equation has been obtained by Homotopy Perturbation Method. Potential of prescribed semi analytical technique is specifically examined for (3+1)-dimensional non-linear Burgers' equation with very small kinematic viscosity factor has not been considered yet. Numerical experiments with illustrated absolute error and 3D graphical presentation testify the reliability of the technique. All the computational procedure has been done using MATLAB.
  • Classification : 65H20, 65N12, 65N15, 35C10
  • Format : Online Talk on Zoom
  • Author(s) :
    • Shelly Arora (Punjabi University, Patiala)
    • Atul Pasrija (Punjabi University, Patiala)
    • Sukhjit Singh Dhaliwal (SLIET, Longowal)

[02614] Convergence of a Second-Order Scheme for Nonlocal Traffic Flow Problems

  • Session Time & Room : 4E (Aug.24, 17:40-19:20) @E506
  • Type : Contributed Talk
  • Abstract : In this work, we focus on the construction and convergence analysis of a second-order numerical scheme for traffic flow models that incorporate non-local conservation laws to capture the interaction between drivers and the surrounding density of vehicles. Specifically, we combine MUSCL-type spatial reconstruction with strong stability preserving Runge-Kutta time-stepping to devise a fully discrete second-order scheme for these equations. We show that this scheme satisfies a maximum principle and obtain bounded variation estimates. Also, the scheme is shown to admit L1- Lipschitz continuity in time. Subsequently, employing the Kolmogorov's theorem with a modification and using a Lax-Wendroff type argument, the convergence of this scheme to the entropy solution of the underlying problem is established. Numerical examples are presented to validate our theoretical analysis. Additionally, we extend our analysis to two dimensional non-local problems, for which we present a positivity preserving second-order scheme. While first-order methods are typically reliable in computational fluid dynamics, higher-order methods can provide more accurate solutions at the same computational cost, especially for problems in two or three dimensions. Our proposed scheme thus has important implications for accurately approximating traffic flow equations, and our theoretical analysis provides a solid foundation for its practical implementation.
  • Classification : 35L65, 65M12, 65M08
  • Format : Talk at Waseda University
  • Author(s) :
    • Nikhil Manoj (Indian Institute of Science Education and Research, Thiruvananthapuram)
    • Sudarshan Kumar K (IISER Thiruvananthapuram)
    • GD Veerappa Gowda (Center for Applicable Mathematics, TIFR Bangalore)

[00028] Riemann problem for the Chaplygin gas equations for several classes of non-constant initial data

  • Session Time & Room : 4E (Aug.24, 17:40-19:20) @E506
  • Type : Contributed Talk
  • Abstract : Using the differential constraint method, a class of exact solutions is obtained for the homogeneous quasilinear hyperbolic system of partial differential equations describing Chaplygin gas equation; these solutions exhibit linearly degenerate that leads to the formation of contact discontinuities. In fact, in this paper, we solved the gen- eralized Riemann problem through a characteristic shock(s). For several classes of non-constant and smooth initial data, the solution to the generalized Riemann problem is presented.
  • Classification : 35L67
  • Format : Talk at Waseda University
  • Author(s) :
    • Akshay Kumar (University of Hyderabad)
    • Radha R (University of Hyderabad)