Registered Data
Contents
- 1 [CT099]
- 1.1 [01283] Global Convergence Domains for Fredholm Integral Equations
- 1.2 [00889] Multiple-Relaxation Runge Kutta Methods for Conservative Dynamical Systems
- 1.3 [00907] Taylor-Fourier integrators
- 1.4 [00903] Port-Hamiltonian form and stochastic Galerkin method for ordinary differential equations
- 1.5 [02106] Numerical solver of ordinary differential equations based on IMT-DE variable transformation
[CT099]
[01283] Global Convergence Domains for Fredholm Integral Equations
- 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 )
[00889] Multiple-Relaxation Runge Kutta Methods for Conservative Dynamical Systems
- 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))
[00907] Taylor-Fourier integrators
- 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)
[00903] Port-Hamiltonian form and stochastic Galerkin method for ordinary differential equations
- 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)
[02106] Numerical solver of ordinary differential equations based on IMT-DE variable transformation
- 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)