Concept

Stiff equation

Related lectures (31)

Multistep methods

Covers multistep methods for solving differential equations, focusing on stability conditions and examples.

Runge Kutta and Multistep Methods

Explores Runge Kutta and multistep methods for solving ODEs, including Backward Euler and Crank-Nicolson.

System of ODEs

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

Numerics: semester project

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

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.

Concept of Stability in ODEs

Explores stability in ODEs, including error checks, equilibrium points, and global attractors, with a focus on numerical schemes like Euler's method.

Stiff Systems: Understanding ODEs with Different Time Scales

Covers stiff systems in ODEs with different time scales and numerical integration methods.

Galerkin Method: Applications and Formulation

Explores the Galerkin method's applications in solving structural problems with a focus on rigidity and forces.

Optimization methods

Covers optimization methods, focusing on gradient methods and line search techniques.

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.

Elasto-Gravity Bending: Energy and Equilibrium

Explores elasto-gravity bending in thin sheets, covering bending energy, equilibrium shapes, and numerical methods.

Isoparametric Formulation of Quad4 Element

Covers the isoparametric formulation of the Quad4 planar element and stiffness matrix calculation.

Absolute Stability in Digital Analysis

Explores absolute stability in digital analysis and Euler's methods through numerical schemes and verification processes.

Convergence Analysis: Explicit RK Scheme

Explores the convergence analysis of the Explicit Runge-Kutta scheme for accurate numerical solutions.

Iso-parametric Formulation of Quad4 Element

Explains the iso-parametric formulation of the quad4 planar element and the calculation of the stiffness matrix.

Absolute Stability in Numerical Methods

Explores absolute stability in numerical methods, emphasizing the control of disturbances in the solution.

Ordinary Differential Equations: Stability

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

Stability of EP: Absolute Stability Property

Covers the concept of absolute stability property and stability conditions in EP.

Ordinary Differential Equations: Methods and Accuracy

Introduces methods for solving ordinary differential equations and discusses their accuracy and limitations.

ODE Solvers: Runge-Kutta, Multistep Methods

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