Lectures related to Explicit and implicit methods

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

Covers Euler and Crank-Nicolson methods for solving differential equations.

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

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

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

Covers ordinary differential equations with a focus on implicit schemes and Euler retrograde.

Explores numerical methods for unsteady flow simulation, emphasizing time integration techniques and boundedness criteria.

Discusses the variational formulation of the heat equation using the finite element method.

Covers the application of Newmark schemes for time discretization in the context of energy conservation.

Explores methods for ordinary differential equations and the importance of Lipschitz continuity in ensuring unique solutions.

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

Discusses degrees of freedom analysis and solving methods in energy conversion flowsheets.

Covers the retrograde Euler method, an implicit numerical scheme used to solve equations and the concept of convergence order.

Explores optimal transport, gradient flows, the implicit Euler scheme, and the heat equation in the context of Dirichlet energy functional.

Discusses the stability of the Newmark-B method and time integration with external forces.

Explores the Cauchy problem and Euler methods for numerical solutions in ODEs.

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

Explores absolute stability in autonomous differential equation systems and the properties of equilibrium points and attractors.

Explores implicit and explicit methods in numerical analysis using Euler's paths.

Explores nonlinear analysis of structures, including the Newmark Method and modeling strategies.