Titolo Unità Formativa |
Unità Didattica |
2D Convection-diffusion equation | Parabolic equations in two and three space dimensions |
2D DuFort-Frankel method | Parabolic equations in two and three space dimensions |
2D implicit methods | Parabolic equations in two and three space dimensions |
A noteworthy eigenvalue-eigenvector property | Matlab interlude 4 |
A simple implicit method | Parabolic equations. Von Neumann stability |
Algebraic operations | Matlab Interlude 1 |
An example of unstable method | Parabolic equations. Von Neumann stability |
Analysis of consistency | Parabolic equations. Von Neumann stability |
AND operator | Matlab interlude 3 |
Another implicit method for the wave equation | Wave equation |
Applications | An explicit finite-difference method |
Approximation for higher-order derivatives | Finite differences |
Approximation for mixed derivatives | Finite differences |
Block matrices | Elements of linear algebra |
Boundary conditions | Fourier model of heat conduction |
Boundary conditions of the second kind | Parabolic equations in two and three space dimensions |
Calling a function | Matlab interlude 2 |
Central approximations | Finite differences |
Cfl1 function | Matlab interlude 9 |
Cfl1 function: Subfunctions and Notes | Matlab interlude 9 |
Cfl4 function | Matlab interlude 9 |
Classical explicit method | An explicit finite-difference method |
Classification of second-order PDEs | Classification of PDEs |
Classification of systems of first order | Classification of PDEs |
Combined scheme | Parabolic equations. Von Neumann stability |
Condif1 function | Matlab interlude 7 |
Condif1 function: subfunctions | Matlab interlude 7 |
Condif2D1 function: finite differences | Matlab interlude 8 |
Condif2D1 function: initialization | Matlab interlude 8 |
Condif2D1 function: numerical background | Matlab interlude 8 |
Condif2D1 function: subfunctions | Matlab interlude 8 |
Condif2D2 function: numerical background | Matlab interlude 8 |
Condif2D2 function: the code (part I) | Matlab interlude 8 |
Condif2D2 function: the code (part II) | Matlab interlude 8 |
Consistency | An explicit finite-difference method |
Convection-diffusion equation | Parabolic equations. Matrix stability |
Convergence | An explicit finite-difference method |
Courant-Friederichs-Lewy method | Wave equation |
Crank function | Matlab interlude 6 |
Crank function: subfunctions | Matlab interlude 6 |
Crank-Nicolson implicit method | Wave equation |
Crank-Nicolson method | Parabolic equations. Von Neumann stability |
Creating matrices | Matlab Interlude 1 |
Diffusion in moving media | Fourier model of heat conduction |
Dirichlet problem | Parabolic equations in two and three space dimensions |
Dirichlet problem | An explicit finite-difference method |
Dirichlet problem for the wave equation | Wave equation |
Discrete functions | Finite differences |
DuFort-Frankel method | Parabolic equations. Von Neumann stability |
Dufort1 function: finite differences and subfunctions | Matlab interlude 6 |
Dufort1 function: initialization | Matlab interlude 6 |
Dufort2D function | Matlab interlude 8 |
Dufort2D function: Subfunctions | Matlab interlude 8 |
Eigenvalues and eigenvectors | Elements of linear algebra |
Energy balance | Fourier model of heat conduction |
Equation for traffic flow | Hyperbolic equations |
Equations of second order with n independent variables | Classification of PDEs |
Example 1 | Matlab Interlude 1 |
Example 1 (Subfunctions and Notes) | Matlab interlude 3 |
Example 2 | Matlab interlude 3 |
Example 2 | Matlab Interlude 1 |
Example 2 (Subfunctions and Notes) | Matlab interlude 3 |
Example 3 | Matlab Interlude 1 |
Example 4 | Matlab Interlude 1 |
Example of convergent method | An explicit finite-difference method |
Examples of matrix norms | Elements of linear algebra |
Executing the function | Matlab interlude 2 |
Fick's law and diffusion | Fourier model of heat conduction |
Finite-difference applications: Example 1 | Matlab interlude 3 |
First-order equations | Hyperbolic equations |
Flexible strings | Wave equation |
Flow control structures: if statement | Matlab interlude 2 |
Flow control structures: switch statement | Matlab interlude 2 |
Flow control structures: while loop | Matlab interlude 2 |
Forward and backward approximations | Finite differences |
Fourier law | Fourier model of heat conduction |
Ftbs function | Matlab interlude 10 |
Ftbs function: Finite-difference method | Matlab interlude 10 |
Function files | Matlab interlude 2 |
Function with multiple output variable | Matlab interlude 2 |
Functions in two variables | Finite differences |
Generating eigenvalues and spectral radius | Matlab interlude 4 |
Generating eigenvectors | Matlab interlude 4 |
Generating norms | Matlab interlude 4 |
Gerschgorin's theorem | Elements of linear algebra |
Heat equation | Fourier model of heat conduction |
Heat equation in two and three space dimensions | Parabolic equations in two and three space dimensions |
Heat2D1 function: Notes | Matlab interlude 8 |
Heat2D1 function: Part I | Matlab interlude 8 |
Heat2D1 function: Part II | Matlab interlude 8 |
Hyperbolic model of heat conduction | Hyperbolic equations |
If statement: Example 1 | Matlab interlude 2 |
If statement: Example 2. Relational operators | Matlab interlude 2 |
If statement: Examples 3 and 4 | Matlab interlude 2 |
Initial-boundary conditions | Wave equation |
Initial-boundary conditions | Matlab interlude 10 |
Introduction to stability | An explicit finite-difference method |
Lax-Friederichs and MacCormack methods | Hyperbolic equations |
Lax-Friederichs method | Hyperbolic equations |
Lax-Wendroff method | Hyperbolic equations |
Lax-Wendroff method for nonlinear systems | Hyperbolic equations |
Lax-Wendroff method for systems | Hyperbolic equations |
Left division | Matlab Interlude 1 |
Local equations | Wave equation |
Logical functions | Matlab interlude 3 |
Logical operators | Matlab interlude 3 |
Mac function (Part I) | Matlab interlude 10 |
Mac function (Part II) | Matlab interlude 10 |
MacCormack method | Hyperbolic equations |
MacCormack system for the wave equation | Matlab interlude 10 |
Matrix form for Robin problem | An explicit finite-difference method |
Matrix manipulations | Matlab Interlude 1 |
Matrix norms | Elements of linear algebra |
Matrix stability | Parabolic equations. Matrix stability |
Matrix stability conditions | Parabolic equations. Matrix stability |
Method of lines | Parabolic equations. Matrix stability |
Mol1 function | Matlab interlude 7 |
Mol2 function | Matlab interlude 7 |
Mol3 function: code | Matlab interlude 7 |
Mol3 function: computational background | Matlab interlude 7 |
Neumann boundary conditions | An explicit finite-difference method |
Neumann problem in matrix notations | An explicit finite-difference method |
Non-dimensional form of the heat equation | An explicit finite-difference method |
Nonlinear equation | Parabolic equations. Matrix stability |
Nonlinear systems. Conservative form | Hyperbolic equations |
Noteworthy equations | Classification of PDEs |
One-dimensional boundary conditions | Fourier model of heat conduction |
One-dimensional continuum | Wave equation |
OR and NOT operators | Matlab interlude 3 |
Partial differential equation of first order | Classification of PDEs |
Phase-change problems | Fourier model of heat conduction |
Physical processes depending on time | Fourier model of heat conduction |
Porous media and Darcy's law | Fourier model of heat conduction |
Richardson function | Matlab interlude 6 |
Robin problem | An explicit finite-difference method |
Saturated fluids | Fourier model of heat conduction |
Saving and appending | Matlab interlude 5 |
Saving graphs. Copying and pasting | Matlab interlude 5 |
Script files | Matlab Interlude 1 |
Second-order partial differential equations | Classification of PDEs |
Simple function | Matlab interlude 6 |
Simple function: subfunctions | Matlab interlude 6 |
Spectral radius | Elements of linear algebra |
Stability analysis | An explicit finite-difference method |
Stability analysis for nonlinear equations | Parabolic equations. Matrix stability |
Stefan condition | Fourier model of heat conduction |
Subfunctions | Matlab interlude 2 |
Submatrices | Matlab Interlude 1 |
Switch structure: Example 1 | Matlab interlude 2 |
Switch structure: Example 2 | Matlab interlude 2 |
Systems of first-order equations | Hyperbolic equations |
Systems of first-order PDEs | Classification of PDEs |
The load function. Import Wizard | Matlab interlude 5 |
The save function | Matlab interlude 5 |
Three-point approximations | Finite differences |
Three-time-level method | Hyperbolic equations |
Tridiagonal matrices | Matlab Interlude 1 |
Tridiagonal matrices | Elements of linear algebra |
Useful commands | Matlab interlude 4 |
Useful commands for functions. Exercises | Matlab interlude 2 |
Variable coefficients | Parabolic equations. Matrix stability |
Vector norms | Elements of linear algebra |
Von Neumann criterion | Parabolic equations. Von Neumann stability |
Von Neumann stability | Parabolic equations. Von Neumann stability |
Wave equation | Wave equation |
Wave1 function | Matlab interlude 9 |
Wave1 function: Subfunctions and Notes | Matlab interlude 9 |
Wendroff function | Matlab interlude 10 |
Wendroff function: Subfunctions and Notes | Matlab interlude 10 |
While loop: Exercises | Matlab interlude 2 |