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[CT100]

Session Date & Time : 2E (Aug.22, 17:40-19:20)
Type : Contributed Talk
Abstract : Dahlquist's First Stability Barrier limits the order of stable $k$-step multistep methods, allowing us to add free parameters. Within the parameter domain where a $k$-step family of methods is stable, we explore the parameters' effect on error and stability domains. For first-order IVP's, we investigate explicit methods for $k=2,3$ and implicit methods for $k=3,4$, generalizing Adams & BDF methods. For second-order IVP's, we analyze explicit and implicit methods for $k=3,4$, generalizing Störmer & Cowell methods.
Classification : 65L06, 65L07, 65L20
Author(s) :
- Michelle Ghrist (Gonzaga University)
- Ben Lombardi (Gonzaga University)
- Alana Marie Dillinger (Twin Cities in Motion)

Session Date & Time : 2E (Aug.22, 17:40-19:20)
Type : Contributed Talk
Abstract : The singularly perturbed differential equation is characterized by a parameter, which multiplies the highest order derivative term in the equation. The solutions of this class of differential equations change rapidly in narrow regions. An orthogonal spline collocation method (OSCM) with C1 splines of degree r ≥ 3 is analyzed for the numerical solution of singularly perturbed reaction diffusion problems in one dimension. The method is applied on a Shishkin mesh and quasi-optimal error estimates in weighted Hm norms for m = 1,2 and in discrete L2-norm are derived.
Classification : 65L08
Author(s) :
- kapil k sharma (south asian university)

Session Date & Time : 2E (Aug.22, 17:40-19:20)
Type : Contributed Talk
Abstract : The leapfrog algorithm was proposed in Noakes’98 to find geodesics joining two given points $x_0$ and $x_1$ on a path-connected complete Riemannian manifold. The basic idea is to choose some junctions between $x_0$ and $x_1$ that can be joined by geodesics locally and then adjust these junctions. In this talk, we find the relationship between the leapfrog's convergence rate $\tau_{i,n}$ of $i$-th junction with the maximal root $\lambda_n$ of a polynomial.
Classification : 65L10, 65D15, 49J45, 53C22
Author(s) :
- Erchuan Zhang (University of Western Australia)
- Lyle Noakes (University of Western Australia)

Session Date & Time : 2E (Aug.22, 17:40-19:20)
Type : Contributed Talk
Abstract : In this work, a thorough investigation of the transient magnetohydrodynamic Navier-Stokes (MHD-NS) equations is carried out applying variational multiscale stabilized finite element (VMSFE) technique. The convergence characteristics of VMSFE scheme (Apriori Estimate) has been derived in this study. The VMSFE method's credibility is stablished by numerical experiments on multiply driven cavity flow. The flow pattern is traced for various Hartmann, Reynolds, and magnetic force inclination angle values.
Classification : 65L60, 65K15
Author(s) :
- Anil Rathi (Indian Institute of Technology, Kanpur (India))
- B.V. Rathish Kumar (Indian Institute of Technology, Kanpur (India))
- Dipak Kumar Sahoo (Indian Institute of Technology, Kanpur)

Session Date & Time : 2E (Aug.22, 17:40-19:20)
Type : Contributed Talk
Abstract : This work addresses the reaction-diffusion system involving coupled partial differential equations. The system explains cancer invasion and transmission mechanisms inside the host. The Galerkin finite element scheme and the second-order backward differential formula (BDF2) are implemented in the given system of equations for spatial and temporal discretization, respectively. Further, a priori error bounds and convergence estimates for the fully-discrete problem are derived. Numerical tests are given to validate the theoretical studies.
Classification : 65L60, 40G05, 35N99
Author(s) :
- Manimaran Jeyaraj (Assistant Professor)
- Shangerganesh Lingeshwaran (National Institute of Technology Goa)