Registered Data

[CT091]

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

  • Session Date & Time : 4E (Aug.24, 17:40-19:20)
  • 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
  • Author(s) :
    • Daniel Bussell (UCL)

[00318] Efficient iterative methods for solving systems of nonlinear equations

  • Session Date & Time : 4E (Aug.24, 17:40-19:20)
  • Type : Contributed Talk
  • Abstract : The aim of this talk is to discuss the iterative methods for solving system of nonlinear equations. Many problems in Science and Engineering lead to solve a system of nonlinear equations. Solving such equations with the use of analytic methods is almost impossible, so one has to rely on iterative methods. One of the basic scheme to solve such problems is the Newton-Raphson’s method. Based on Newton-Raphson’s iterative scheme many higher order and computationally efficient methods have been derived in the literature. These methods have been used to solve Hammerstein's integral equation, boundary value problems, Burger's equation and many more such type of equations. Moreover, these methods can solve system of equations with large number of equations. But Newton-Raphson's method and the methods based on this have one drawback that they require the evaluation of the derivative. So, keeping this in mind many methods have derived in the literature which are derivative free and use only function evaluations. In these methods, the derivative is approximated by their divided difference approximation. The basic method in this category is the Traub-steffensen's method. This talk will present recent work in this area and will contain the following topics: - iterative methods with derivative - iterative methods without derivative - implementation on numerical problems like integral equations, ODES and PDES - discussion on efficiency of these methods
  • Classification : 65H10, 65Y20, 41A58
  • Author(s) :
    • Himani Arora (Guru Nanak Dev University, Amritsar, Punjab)
    • Arvind Mahindru (DAV University, Jalandhar)

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

  • Session Date & Time : 4E (Aug.24, 17:40-19:20)
  • 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
  • Author(s) :
    • Sonia Bhalla (Chandigarh University)

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

  • Session Date & Time : 4E (Aug.24, 17:40-19:20)
  • 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
  • Author(s) :
    • Shelly Arora (Punjabi University, Patiala)
    • Atul Pasrija (Punjabi University, Patiala)
    • Sukhjit Singh Dhaliwal (SLIET, Longowal)

[00548] Selection of Linear Operator and Initial Guess for Homotopy Methods

  • Session Date & Time : 4E (Aug.24, 17:40-19:20)
  • Type : Contributed Talk
  • Abstract : We propose an algorithm for the selection of auxiliary linear operator L(u) and initial guess, where the coefficients of derivatives involved in L(u) are functions of auxiliary roots of L(u) = 0. Based on residual error minimization, we compute these unknown root s. This ensures the convergence of our semi-analytical series solution using the basic Homotopy Analysis/Perturbation Method without any artificial parameters. We compared our technique's accuracy and efficiency to other existing analytical and numerical methods.
  • Classification : 65H20
  • Author(s) :
    • Dilip Kumar Maiti (Dept of Applied Mathematics with Oceanology and Computer Programming. Vidyasagar University, Midnapur, WB, INDIA)
    • Tapas Roy (Vidyasagar University)