Search for tag: "hyperbolic"

Hyperbolic PDE Analytical methods Example 2: Separation of variables example 9.14

Step by step solution of both cases from example 9.14. This example uses the method of separation of variables on the wave equation.

From  Daniel Friedrich on March 1st, 2021 0 likes 47 plays 0  

Hyperbolic PDE Analytical methods Part 6: Separation of variables

This video introduces the method of separation of variables or separated solutions for the wave equation.

From  Daniel Friedrich on March 1st, 2021 0 likes 44 plays 0  

Hyperbolic PDE Analytical methods Example 1: Characteristics example 9.13

Step by step solution of example 9.13 which covers a wave equation problem solved by the method of characteristics.

From  Daniel Friedrich on March 1st, 2021 0 likes 56 plays 0  

Partial Differential Equations Lecture 10 - Boundary Conditions

In the 2nd part of the lecture we look at boundary conditions for systems of hyperbolic equations.

From  David Ingram on February 26th, 2021 0 likes 31 plays 0  

Hyperbolic PDE Analytical methods Part 4: Method of characteristics

Introduce the method of characteristics for hyperbolic PDEs

From  Daniel Friedrich on February 22nd, 2021 0 likes 68 plays 0  

Partial Differential Equations Lecture 9 - Results

Here we look in detail at the results from the test problem and discuss dispersive and dissipative errors.

From  David Ingram on February 16th, 2021 0 likes 26 plays 0  

Partial Differential Equations Lecture 9 - MacCormack method in 2D

This part of the lecture develops a 2D solver using the method of Fractional Steps and the MacCormack scheme and applies it to a test problem

From  David Ingram on February 16th, 2021 0 likes 32 plays 0  

Partial Differential Equations Lecture 9 - Two and three dimensional solvers

In this lecture we look at operator splitting and the method of fractional steps which can be used to solve 2 and 3D problems with 1D schemes.

From  David Ingram on February 16th, 2021 0 likes 32 plays 0  

Hyperbolic PDE Analytical methods Part 3: D'Alembert solution

This video derives the d'Alembert solution for the hyperbolic wave equation.

From  Daniel Friedrich on February 16th, 2021 0 likes 67 plays 0  

Hyperbolic PDE Analytical methods Part 2: Vibrating string and linear advection

This video shows that two expressions are solutions to the wave equation for two different conditions: 1) the fundamental mode of the vibrating string and 2) the linear advection problem.

From  Daniel Friedrich on February 16th, 2021 0 likes 62 plays 0  

Hyperbolic PDE Analytical methods Part 1: Introduction

Introduction to the hyperbolic wave equation and derivation of the 1D wave equation.

From  Daniel Friedrich on February 16th, 2021 0 likes 70 plays 0  

Partial Differential Equations, Lecture 8c: MUSCL Schemes

We look briefly at how MUSCL schemes use weighted interpolation of fluxes as an alternative to the TVD schemes.

From  David Ingram on February 15th, 2021 0 likes 29 plays 0  

Partial Differential Equations, Lecture 8b: TVD MacCormack

Here we implement the MacCormack scheme with a TVD correction in Matlab and apply it to a test problem

From  David Ingram on February 15th, 2021 0 likes 34 plays 0  

Partial Differential Equations, Lecture 8a: Monotone Methods for Conservation Laws

In this lecture we look at schemes which are not prone to producing the spurious "Gibbs" oscillations we saw in the last lecture. We start b talking about TVD schemes

From  David Ingram on February 15th, 2021 0 likes 32 plays 0  

Partial Differential Equations, Lecture 7a: Numerical solution of hyperbolic PDEs.

A lecture introducing numerical methods for hyperbolic PDEs

From  David Ingram on February 8th, 2021 0 likes 37 plays 0