Runge–Kutta methods

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Error Estimation in Numerical Methods

Explores error estimation in numerical methods for solving ordinary differential equations, emphasizing the impact of errors on solution accuracy and stability.

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Covers the semester project on numerics, focusing on adaptive algorithms and multistep methods.

Runge-Kutta Methods: Stability and Implicit Schemes

Explores digital integration methods, stability, and implicit schemes in Runge-Kutta methods.

ODE Solvers: Runge-Kutta, Multistep Methods

Explores Runge-Kutta and multistep methods for solving ODEs, comparing their accuracy and efficiency.

Numerical Integration: Euler Method

Covers the progressive Euler method for numerical integration of ODEs, including Cauchy problems and Runge-Kutta methods.

Explicit Stabilised Methods: Stochastic Differential Equations

Covers explicit stabilized methods for stiff stochastic differential equations, analyzing their properties and applications.

Euler Backward Method: ODEs

Explores the Euler backward method for ODEs, discussing stability, error reduction, and implicit vs explicit methods.

Ordinary Differential Equations: Methods and Applications

Explores ordinary differential equations and numerical integration methods for stability and accuracy.

Optimal Transport: Gradient Flows in Rd

Explores optimal transport and gradient flows in Rd, emphasizing convergence and the role of Lipschitz and Picard-Lindelöf theorems.

Explicit RK Methods

Explains explicit Runge-Kutta methods up to order 4 and conditions for method's order.