Advection-Diffusion Equations

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Finite Differences in Advection-Diffusion

Explores the explicit 2-level scheme for advection-diffusion and the convergence of digital solutions.

Numerical Differentiation: Part 1

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

Numerical Methods in Chemistry

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

Wave Equations Stability

Explores resonant shallow water equations, stability analysis, eigenmodes, and clean modes in waves.

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.

Thomas algorithm, accuracy of direct methods

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

Numerical Methods: Boundary Value Problems

Explores boundary value problems, finite difference method, and Joule heating examples in 1D.

Numerical Methods: Euler and Crank-Nicolson

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

Numerical Differentiation: Backward and Central Differences

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

Numerical Integration Methods

Explores numerical integration methods and their application in solving differential equations and simulating physical systems.