Lectures related to Ill-posed Numerical Problems

Explores backward and central differences for numerical differentiation, analyzing their properties and error analysis.

Introduces the Euler Forward Method for ODEs, focusing on error analysis and stability.

Covers Ordinary Differential Equations, first-order solutions, and numerical methods for IVP and BVP.

Covers open methods, Newton-Raphson, and secant method for iterative solutions in numerical methods.

Covers the derivation of multi-group diffusion equations and the numerical methods for solving the neutron diffusion equation.

Explores the sensitivity of solutions in numerical methods, including linear systems and matrix norms, with an example of deblurring images.

Explains Lagrange interpolation for numerical integration and introduces Simpson's rules.

Explores the concepts of linear and quadratic convergence rates, highlighting their differences and applications in numerical methods.

Explores unconfined flow in computational geomechanics, emphasizing weak form derivation and relative permeability.

Discusses the explicit Runge Kulta method for function approximation and error analysis.

Explores floating point numbers, LU decomposition, errors in numerical computations, and the impact of round-off errors.

Covers Richardson extrapolation for numerical differentiation to reduce error.

Explores the Thomas algorithm for tridiagonal systems and the accuracy of direct methods in numerical computations.

Focuses on numerical modelling of atmospheric processes to predict weather and climate phenomena, covering key concepts and methods.

Covers the verification and validation process in numerical flow simulation, ensuring credibility of simulation outcomes.

Discusses evaluation feedback, convergence, error analysis, and adaptive time steps in physics simulations.

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

Explores iterative numerical methods for solving equations, emphasizing convergence criteria, errors, and starting values' impact.

Explores consistency and stability in numerical methods, emphasizing error analysis and the role of boundary conditions.

Covers the numerical approach to derivative calculation, focusing on formulas and methods such as fine differences.