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[CT099]

Session Time & Room : 2E (Aug.22, 17:40-19:20) @E505
Type : Contributed Talk
Abstract : We consider systems of ordinary differential equations (ODEs) including random variables. Based on a polynomial chaos expansion, a stochastic Galerkin approach yields a larger deterministic system of ODEs. We investigate port-Hamiltonian formulations of the original systems and the Galerkin systems. A structure-preserving stochastic Galerkin projection is constructed, which produces a larger port-Hamiltonian system. Furthermore, the associated Hamiltonian functions are compared. We present results of numerical computations using a test example.
Classification : 65L05, 34F05, uncertainty quantification
Format : Talk at Waseda University
Author(s) :
- Roland Pulch (University of Greifswald)

Session Time & Room : 2E (Aug.22, 17:40-19:20) @E505
Type : Contributed Talk
Abstract : We propose a numerical solver of initial value problems of ordinary differential equations based on the IMT-DE variable transformation, a variant of the transformation of the IMT quadrature formula. We solve the Volterra integral equation equivalent to the initial value problem by the Picard iteration, which is numerically executed by the numerical indefinite integration based on the IMT-DE transformation. This study is an example of the applications of the IMT type transformations to various computations.
Classification : 65L05, 65R20, 65D30
Format : Talk at Waseda University
Author(s) :
- Hidenori Ogata (The University of Electro-Communications)

Session Time & Room : 2E (Aug.22, 17:40-19:20) @E505
Type : Contributed Talk
Abstract : Relaxation Runge-Kutta methods, which are a slight modification of the RK methods, have been introduced to preserve invariants of initial-value problems. So far, this approach has been applied to preserve only one nonlinear functional in the numerical solution of a problem. In this talk, I will present the generalization of the relaxation approach for RK methods to preserve multiple nonlinear invariants of a dynamical system. The significance of preserving multiple invariants and its impact on long-term error growth will be illustrated via several numerical examples.
Classification : 65L04, 65L20, 65M06, 65M12, 65M22
Format : Talk at Waseda University
Author(s) :
- Abhijit Biswas (King Abdullah University of Science and Technology (KAUST))
- David Isaac Ketcheson (King Abdullah University of Science and Technology (KAUST))

Session Time & Room : 2E (Aug.22, 17:40-19:20) @E505
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 Time & Room : 2E (Aug.22, 17:40-19:20) @E505
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
Format : Online Talk on Zoom
Author(s) :
- Erchuan Zhang (University of Western Australia)
- Lyle Noakes (University of Western Australia)