High order operator-splitting method for the numerical time propagation of the full Boltzmann equation in the interaction picture

• Main Author: Zadzaan Bin Hassan
• Other Authors: Marco Battiato
• Format: Final Year Project
• Language: English
• Published: Nanyang Technological University 2023
• Subjects: Science::Mathematics::Applied mathematics::Numerical analysis; Science::Physics::Atomic physics::Statistical physics
• Online Access: https://hdl.handle.net/10356/166536
• Institution: Nanyang Technological University

This thesis focuses on finding a suitable high order splitting method for the numerical time propagation of the Boltzmann equation in the interaction method. Using Runge-Kutta family of numerical methods to create an adaptive step method in the interaction method to solve both collision and transport term of the Boltzmann equation. The numerical method of Runge-Kutta 4 and Dormand-Prince 54 is first derived in their step-adaptive version. Followed by implementing the interaction picture into their step adaptive version. By introducing an Ordinary Differential Equation with similar structure to the Boltzmann, the two methods can be tested to observe on their performance. Next, by comparing the Order of Convergence of Runge-Kutta 4 and Dormand-Prince 54 method, it is found that Dormand Prince 54 method performs more efficient and accurately solving for numerical solution to a Boltzmann-like Ordinary Differential Equation. Lastly, an introduction of using a Dormand-Prince 54 method to calculate the product of a vector and exponential matrix rather than approximating the exponential matrix is shown to shorten computational time.