## Numerical Studies of Korteweg-de Vries Equation with Random Input Data

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Differential equations are primary tools to mathematically model physical phenomena in industry and natural science and to gain knowledge about its features. However, classical deterministic differential equations does not sufficiently model physically observed phenomena since there exit naturally inevitable uncertainties in nature. Employing random variables or processes as inputs or coefficients of the differential equations yields a stochastic differential equation which can clarify unnoticed features of the physical events. Korteweg-de Vries (KdV) equation with random input data is a fundamental differential equation for modeling and describing solitary waves occurring in nature. It can be represented by employing time dependent additive randomness into its forcing or space dependent multiplicative randomness into derivative of the solution. Since analytical solutions of the differential equation with the random data input does not exist, quantifying and propagating uncertainty employed on the differential equation are done by numerical approximation techniques. This project focus on a numerical investigation of the Korteweg-de Vries equation with random input data.

Collaborators

- Hamdullah Yücel, Institute of Applied Mathematics, METU (Director)
- Pelin Çiloğlu, Institute of Applied Mathematics, METU (Researcher)
- M. Alp Üreten, Institute of Applied Mathematics, METU (Researcher)

Funded by BAP: YÖP-705-2018-2820, May 29 2018 - May 29 2019.

Scientific Activities

**October 21, 2018:**Pelin Çiloğlu gives a research talk, titled "Discontinuous Galerkin Methods for Unsteady Convection Diffusion Equation with Random Coefficients" in BEYOND: Workshop on Computational Science and Engineering**.****September 24, 2018:**Pelin Çiloğlu gives a research talk, titled "Unsteady Convection Diffusion Equation with Random Input Data" in the Chemnitz FE Symposium 2018.**September 03, 2018**: M. Alp Üreten successfully defends his Master thesis, titled "Numerical Studies of Korteweg-de Vries Equation with Random Input Data".