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1 [CT101]

[CT101]

[00013] Singularly perturbed problems on a graph

Session Date & Time : 3D (Aug.23, 15:30-17:10)
Type : Contributed Talk
Abstract : In this talk, a singularly perturbed convection diffusion problems on a graph domain will be discussed. Initially, the problem is designed on a simple graph i.e k-star graph. On the common vertex, the continuity and the Kirchhoff's conditions will be discussed along with their complexity. The problem may be extended to a general graph with many vertices and edges. Some tests problems will be discussed based on upwind finite difference methods using piece-wise Shishkin meshes. Error estimates and the order of convergence are to be discussed.
Classification : 65Lxx, 65Mxx
Author(s) :
- Vivek Kumar Aggarwal (Delhi Technological University)

[00858] An adaptive spectral method for oscillatory second-order linear ODEs with frequency-independent cost

Session Date & Time : 3D (Aug.23, 15:30-17:10)
Type : Contributed Talk
Abstract : I will introduce an efficient method for solving 2nd order, linear ODEs whose solution may vary between highly oscillatory and slowly changing over the solution interval. Within a marching scheme, the solution is generated either via a nonoscillatory phase function (computed by defect correction), or spectral collocation, whichever is more efficient for the current timestep. With numerical experiments I will show that our algorithm outperforms other state-of-the-art oscillatory solvers and has a frequency-independent runtime.
Classification : 65Lxx, 34E05, 65L60, 34-04, 65Gxx
Author(s) :
- Fruzsina Julia Agocs (Center for Computational Mathematics, Flatiron Institute)
- Alex Harvey Barnett (Center for Computational Mathematics, Flatiron Institute)

[01055] Uniformly Convergent dG method for two dimensional turning point problem

Session Date & Time : 3D (Aug.23, 15:30-17:10)
Type : Contributed Talk
Abstract : In this talk we present a numerical scheme for 2D singularly perturbed convection-diffusion problems with turning points. The proposed numerical scheme consists of discontinuous Galerkin finite element method with generalized Shishkin mesh. The numerical method is shown to be uniformly convergent with respect to the perturbation parameter. The theoretical results are justified by numerical experiments.
Classification : 65Lxx
Author(s) :
- Kumar Rajeev Ranjan (National Institute of Technology Patna)
- Gowrisankar S (National Institute of Technology Patna)

[01151] Structure-Preserving Neural Networks for Hamiltonian Systems

Session Date & Time : 3D (Aug.23, 15:30-17:10)
Type : Contributed Talk
Abstract : When solving Hamiltonian systems using numerical integrators, preserving the symplectic structure is crucial. We analyze whether the same is true if neural networks (NN) are used. In order to include the symplectic structure in the NN's topology we formulate a generalized framework for two well-known NN topologies and discover a novel topology outperforming all others. We find that symplectic NNs generalize better and give more accurate long-term predictions than physics-unaware NNs.
Classification : 65Lxx, 68T07, 85-08
Author(s) :
- Philipp Horn (Eindhoven University of Technology)
- Barry Koren (Eindhoven University of Technology)
- Veronica Saz Ulibarrena (Leiden University)
- Simon Portegies Zwart (Leiden University)

[02339] An iterative analytic approximation to nonlinear reaction–diffusion equations

Session Date & Time : 3D (Aug.23, 15:30-17:10)
Type : Contributed Talk
Abstract : The paper concerns a class of nonlinear reaction-diffusion equations with a dissipating parameter. The problem is singularly perturbed from a mathematical perspective. Solutions to these problems are known to exhibit multiscale character. There are narrow regions in which the solution has a steep gradient. To approximate multiscale solution, we present and analyze an iterative analytic method based on a Lagrange multiplier technique. We obtain closed-form analytic approximation to nonlinear boundary value problems through iteration. The Lagrange multiplier is obtained optimally, in a general setting, using variational theory and Liouville–Green transforms. The paper aims to overcome the well-known difficulties associated with numerical methods. Two test examples are considered, and rigorous comparative analysis is presented. Moreover, we compare the proposed method with others found in the literature.
Classification : 65Lxx
Author(s) :
- Manju Sharma (KVA DAV College, Karnal)
- ADITYA KAUSHIK (Delhi Technological University, Delhi)
- Aastha Gupta (Panjab University, Chandigarh)
- Monika Chaudhary (Delhi Technological University, Delhi)

[02643] A higher-order difference approximation for the system of singularly perturbed reaction-diffusion equations on an equidistributed grid

Session Date & Time : 3E (Aug.23, 17:40-19:20)
Type : Contributed Talk
Abstract : This work presents a higher-order difference method to solve a coupled system of singularly perturbed reaction-diffusion problems over a non-uniform grid. The technique combines cubic and exponential spline difference schemes over an adapted grid generated by equidistributing a non-negative monitor function. The proposed method is numerically stable and uniformly convergent. The convergence obtained is optimal, being free from logarithmic factors. Numerical experiments have been performed and presented for two model problems.
Classification : 65Lxx, 65Mxx, 65Nxx
Author(s) :
- ADITYA KAUSHIK (Delhi Technological University, Delhi)

[01153] Analysis of driver’s behavior and average flow on traffic dynamics

Session Date & Time : 3E (Aug.23, 17:40-19:20)
Type : Contributed Talk
Abstract : In this work, a new lattice model is proposed by considering the driver’s behavior (timid or aggressive) and downstream average flow on traffic dynamics. The stability condition is determined through stability analysis. Nonlinear analysis forms the modified Korteweg-de Vries (mKdV) equation to describe traffic density wave propagation near the critical point. Theoretical results are verified with numerical simulations, and it is concluded that driver behavior and average flow can stabilize traffic flow dynamics.
Classification : 65P40, 65K05, Traffic flow
Author(s) :
- Nikita Madaan (Chandigarh University)
- Nikita Madaan (Thapar Institute of Engineering and Technology)
- Sonia - (Chandigarh University)

[00282] Data Assimilation in Operator Algebras

Session Date & Time : 3E (Aug.23, 17:40-19:20)
Type : Contributed Talk
Abstract : An algebraic framework for data assimilation of dynamical systems and uncertainty quantification is developed. In this framework, the Bayesian formulation of data assimilation is embedded in a non-abelian operator algebra - observables are represented by multiplication operators and probability densities by quantum states. The forecast step is represented by a quantum operation induced by the Koopman operator of the dynamical system. The analysis step is described by a quantum effect. Data-driven implementation uses kernel methods.
Classification : 65P99, 68U99, 47N40, 68T10, 37M99
Author(s) :
- Joanna Maja Slawinska (Dartmouth College, Department of Mathematics)

[00129] Anomalous diffusion in standard maps with extensive chaotic phase spaces

Session Date & Time : 3E (Aug.23, 17:40-19:20)
Type : Contributed Talk
Abstract : In this work, we investigate the long-term diffusion transport and chaos properties of single and coupled standard maps (SMs). We analyze parameters that are known to produce anomalous diffusion in the phase spaces of maps, with the presence of so-called accelerator modes. We study how different ensembles affect the behavior, asymptotic diffusion rates, and time scales required for these maps. We also explore the global diffusion properties and chaotic dynamics of various coupled SM configurations.
Classification : 65Pxx
Author(s) :
- Henok Tenaw Moges (University of Cape Town)
- Henok Tenaw Moges (University of Cape Town)
- Charalampos Skokos (University of Cape Town)

[02022] Use of jet transport for high order methods

Session Date & Time : 3E (Aug.23, 17:40-19:20)
Type : Contributed Talk
Abstract : The use of multivariate polynomial, called jet, in conjunction with numerical solvers, called transport, has recently become a new baseline to address computations based on high order methods. Jet transport provides more accurate, efficient, and reliable results through automatizing several crucial parts. In this talk, I will explain these most recent results and supported by examples in areas in dynamical systems.
Classification : 65Pxx, 37Mxx, 37M21, Numerical integrators for dynamical systems
Author(s) :
- Joan Gimeno (University of Barcelona)
- Angel Jorba (University of Barcelona)
- Marc Jorba (Centre de Recerca Matemàtica)
- Narcís Miguel (PAL Robotics S.L.)
- Maorong Zou (University of Texas at Austin)