Numerical methods for partial differential equations

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Related lectures (30)

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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 Methods for ODEs: Crank-Nicolson, Heun, Euler, RK4

Explores numerical methods like Crank-Nicolson, Heun, Euler, and RK4 for solving ODEs, emphasizing error estimation and convergence.

Direction Fields, Euler Methods, Differential Equations

Explores direction fields, Euler methods, and differential equations through practical exercises and stability analysis.

Numerical Methods for Boundary Value Problems

Covers numerical methods for solving boundary value problems using finite difference, FFT, and finite element methods.

Numerical Methods: Boundary Value Problems

Covers numerical methods for solving boundary value problems, including applications with the Fast Fourier transform (FFT) and de-noising data.

Computational Geomechanics

Covers the basics of computational geomechanics, including poroelasticity, plasticity, and numerical methods for solving geotechnical problems.

Sensitivity of Solutions

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

Stochastic Differential Equations: Mean-Field Inference

Explores inference for stochastic differential equations, focusing on numerical methods and convergence analysis.

Numerical Integration: Lagrange Interpolation, Simpson Rules

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

Error Estimation in Numerical Methods

Explores error estimation in numerical methods for solving differential equations, focusing on local truncation error, stability, and Lipschitz continuity.