Lectures related to Galerkin Orthogonality: Lecture 11

Numerical Modelling of the Atmosphere

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

Thomas algorithm, accuracy of direct methods

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

Numerical Derivation: Formulas and Approaches

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

ODEs: Introduction and Solutions

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

Numerical Differentiation: Part 1

Covers numerical differentiation, forward differences, Taylor's expansion, Big O notation, and error minimization.

Numerical Methods in Biomechanics: Hip-A

Explores numerical methods in biomechanics for hip implants and emphasizes understanding conditions for improved designs and patient outcomes.

Numerical Methods: Iterative Techniques

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

Multigroup Theory: Main Equations and Numerical Solution

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

Numerical Differentiation: Richardson Extrapolation

Covers Richardson extrapolation for numerical differentiation to reduce error.

Numerical Methods in Chemistry

Covers the implementation of numerical methods in MATLAB for solving chemical problems.

Numerical Differentiation: Backward and Central Differences

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

Computational Geomechanics: Unconfined Flow

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

Numerics: semester project

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

System of ODEs

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

Numerical Methods: Euler and Crank-Nicolson

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

Numerical Integration: Lagrange Interpolation, Simpson Rules

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

Numerical Integration: Romberg Integration

Explores Romberg integration to improve numerical integration accuracy through iterative refinement of estimates.

Finite Elements: Elasticity and Variational Formulation

Explores finite element methods for elasticity problems and variational formulations, emphasizing admissible deformations and numerical implementations.

Numerical Analysis: Stability in ODEs

Covers the stability analysis of ODEs using numerical methods and discusses stability conditions.

Verification and validation

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