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Lecture
Runge-Kutta Methods
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Explicit Stabilised Methods: Applications to Bayesian Inverse Problems
Explores explicit stabilised Runge-Kutta methods and their application to Bayesian inverse problems, covering optimization, sampling, and numerical experiments.
Runge-Kutta Methods: Approximating Differential Equations
Covers the stages of the explicit Runge-Kutta method for approximating y(t) with detailed explanations.
Numerical Methods: Euler and Crank-Nicolson
Covers Euler and Crank-Nicolson methods for solving differential equations.
System of ODEs
Explores numerical methods for solving ODE systems, stability regions, and absolute stability importance.
Multistep methods
Covers multistep methods for solving differential equations, focusing on stability conditions and examples.
Optimization methods
Covers optimization methods, focusing on gradient methods and line search techniques.
Numerics: semester project
Covers the semester project on numerics, focusing on adaptive algorithms and multistep methods.
Runge Kutta and Multistep Methods
Explores Runge Kutta and multistep methods for solving ODEs, including Backward Euler and Crank-Nicolson.
High Order Methods: Space Discretisation
Covers high order methods for space discretisation in linear differential systems.
Optimization Methods: Theory Discussion
Explores optimization methods, including unconstrained problems, linear programming, and heuristic approaches.