Corso: Computational Methods for Engineering

 
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Indice Analitico Corso

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