Corso: Computational Methods for Engineering Modulo: Computational PDE with Matlab [home][indice][durata][esci]
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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