Explicit RK Methods

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Related lectures (26)

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Homogeneous Solutions: Linear Independence

Explores finding particular solutions for homogeneous differential equations, emphasizing linear independence and variation of constants.

Phase Portrait and Non-linear Systems

Covers phase portraits, eigenvalue decomposition, Jordan decomposition, and stable nodes in non-linear systems.

Higher Order Methods: Iterative Techniques

Covers higher order methods for solving equations iteratively, including fixed point methods and Newton's method.

Zero-stability and absolute-stability

Explores zero-stability and absolute-stability in numerical methods, including Forward Euler, Backward Euler, Crank-Nicolson, and Heun's methods.

Crank-Nicolson and Heun's Methods

Covers the Crank-Nicolson and Heun's methods, discussing uniqueness of solutions and truncation errors in numerical methods.

Runge-Kutta Methods

Explains the Runge-Kutta methods, particularly the explicit scheme of order 4 (ERK4), and how to optimize parameters for accuracy.

Diffusion-Convection: Modeling and Schemes

Covers modeling and numerical schemes for diffusion-convection problems.

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.

System of ODEs

Explores numerical methods for solving ODE systems, stability regions, and absolute stability importance.

Linear Systems: Convergence and Methods

Explores linear systems, convergence, and solving methods with a focus on CPU time and memory requirements.