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[CT099]

Session Date & Time : 2E (Aug.22, 17:40-19:20)
Type : Contributed Talk
Abstract : The significance of our work is to establish the convergence domains for solving nonlinear Fredholm integral equations of the second kind with non-differentiable Nemytskii operator using iterative methods. Assuming conditions on the Nemytskii operator, we will obtain global convergence domains for the solution of integral equation by using derivative-free improved Chebyshev-Secant-type methods (ICSTM). Numerical examples are worked out to show the applicability of our work, and the results are compared with the existing iterative methods.
Classification : 65L03, 65R10, 65Q20, 45B05, 45L05, Iterative Methods for Solving Non-linear Problems
Author(s) :
- Sukhjit Singh (Dr BR Ambedkar National Institute of Technology Jalandhar India )
- Nisha -- Yadav (Dr BR Ambedkar National Institute of Technology Jalandhar India )

Session Date & Time : 2E (Aug.22, 17:40-19:20)
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
Author(s) :
- Abhijit Biswas (King Abdullah University of Science and Technology (KAUST))
- David Isaac Ketcheson (King Abdullah University of Science and Technology (KAUST))

Session Date & Time : 2E (Aug.22, 17:40-19:20)
Type : Contributed Talk
Abstract : In this talk we study Taylor-Fourier integrators for the numerical solution of differential systems $$\frac{d}{dt}x = A x + g(x),$$ with $g$ a smooth map and $A$ a real matrix whose eigenvalues are integer multiples of an imaginary number $i \omega$, by computing a sequence of approximations to the solution of the differential system $$\frac{d}{dt}y = f(\omega t,y), $$ obtained after making the change of variables $x(t) = e^{tA}y(t)$. Implementation details and numerical results to show the performance of the methods are given.
Classification : 65L04, 65M20
Author(s) :
- Mari Paz Calvo (Universidad de Valladolid)
- Joseba Makazaga (UPV/EHU)
- Ander Murua (UPV/EHU)

Session Date & Time : 2E (Aug.22, 17:40-19:20)
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
Author(s) :
- Roland Pulch (University of Greifswald)

Session Date & Time : 2E (Aug.22, 17:40-19:20)
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
Author(s) :
- Hidenori Ogata (The University of Electro-Communications)