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[CT111]

Session Date & Time : 3E (Aug.23, 17:40-19:20)
Type : Contributed Talk
Abstract : Recently, much attention have paid to energy preserving methods for solving PDE and ODE. One of them is average vector field method (AVF) which is extention of the implicit-mid point rule. In this work, the partitioned energy preserving method (PAVF) is proposed and applied coupled nonlinear Schrödinger (CNLS) equations. The CNLS is discretized in space by using finite difference methods. Application of the PAVF to CNLS equations shows the excellent preservation of the Hamiltonian and momentum in long time integration. Numerical results are compared with those obtained by AVF method.
Classification : 65N06
Author(s) :
- Canan AKKOYUNLU (ISTANBUL KULTUR UNIVERSITY)

Session Date & Time : 3E (Aug.23, 17:40-19:20)
Type : Contributed Talk
Abstract : Moving interface problems are ubiquitous in natural sciences. Often the interface motion is coupled with PDEs in the bulk domain. This talk will present a Cartesian grid-based boundary integral method for solving moving interface problems. Layer potentials are evaluated by solving simple interface problems on a Cartesian grid to take advantage of fast solvers such as FFTs and the geometric multigrid method. Numerical simulations, including crystal growth and two-phase flows, will be reported.
Classification : 65N06, 65R20, 35R35, 80A22
Author(s) :
- Han Zhou (Shanghai Jiao Tong University)
- Wenjun Ying (Shanghai Jiao Tong University)

Session Date & Time : 3E (Aug.23, 17:40-19:20)
Type : Contributed Talk
Abstract : In this work, a novel high-order adaptive algorithm on non-uniform grid points for the Caputo fractional derivative is derived. Developed algorithm allows one to build adaptive nature where numerical scheme is adjusted according to behavior of $\alpha$ to keep errors very small and converge to solution very fast. Analysis of numerical scheme has been established thoroughly. Moreover, a reduced order technique is implemented by using moving mesh refinement to improve accuracy at several time levels.
Classification : 65N06, 65N12, 65N50, 65N15
Author(s) :
- Rahul Kumar Maurya (Government Tilak P.G. College, Katni, Madhya Pradesh, India)
- Vineet Kumar Singh (Indian Institute of Technology (BHU), Varanasi, India)

Session Date & Time : 3E (Aug.23, 17:40-19:20)
Type : Contributed Talk
Abstract : This work develops a stable scheme and adaptive algorithm for time-fractional mathematical models. Developed algorithm allows one to build adaptive nature where numerical scheme is adjusted according to behavior of $\alpha$ to keep errors very small and converge to solution very fast. Analysis of numerical scheme has been established thoroughly. Moreover, a reduced order technique is implemented by using moving mesh refinement to improve accuracy at several time levels.
Classification : 65N06, 65N50, 65N12, 65N15
Author(s) :
- Vineet Kumar Singh (Indian Institute of Technology (BHU), Varanasi, India)
- Rahul Kumar Maurya (Government Tilak P.G. College, Katni, Madhya Pradesh, India)

Session Date & Time : 3E (Aug.23, 17:40-19:20)
Type : Contributed Talk
Abstract : In this talk, we will discuss a new second-order L3 approximation of the Caputo fractional derivative of order 1< α < 2. We have applied Lagrange’s cubic interpolating polynomial to develop this approximation. A second-order difference scheme is also proposed to find the numerical solution of the time-fractional wave equation. The numerical analysis results of the proposed algorithm are provided and a comparative study is also given to show the effectiveness and accuracy of the proposed scheme.
Classification : 65N06
Author(s) :
- NIKHIL SRIVASTAVA (Indian Institute of Technology (BHU) Varanasi, India)