MATH2071_2000 - Numerical Methods in Scientific Computing II

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There is a series of exercises to be done in the lab:

• LAB #1: UNIX
• LAB #2: MATLAB
• LAB #3: Simple ODE Methods
• LAB #4: Explicit ODE Methods
• LAB #5: Implicit ODE Methods
• LAB #6: BVP's and PDE's
• LAB #7: Solving Linear Systems
• LAB #8: Applications of the PLU Factorization
• LAB #9: Norms, Errors, and Condition Numbers
• LAB #10: The QR Factorization
• LAB #11: Solving Special Systems
• LAB #12: The Eigenvalue Problem

Some useful files:

• MOVIE_DEMO.M, make an animation of a set of plots;
• SLINKY.M, y = sin(x)/x;

Algorithm files for lab 1:

• BRANCH.M, a script that uses ROOT;
• ROOT.M, approximates square root;

Algorithm files for lab 2:

• TABLES.M, a sample script file;

Algorithm files for lab 3:

• CHAOTIC_ODE.M, a "chaotic" ODE;
• MODEL_ODE.M, y' = y;
• PENDULUM_LINEAR_ODE.M, a second-order linear ODE for a pendulum;
• PENDULUM_NONLINEAR_ODE.M, a second-order nonlinear ODE for a pendulum;
• PREDATOR_ODE.M, system of 2 ODE's;
• VANDERPOL_ODE.M, van der Pol's heart model;

Algorithm files for lab 4:

• AB2.M, Adams-Bashforth-2 ODE solver;
• EULER_HALFSTEP.M, the Euler halfstep ODE solver;
• MIDPOINT.M, midpoint method ODE solver;
• RK3.M, Runge-Kutta-3 ODE solver;

Algorithm files for lab 5:

• ABM3_PECE.M, ABM3 solver, using PECE method;
• BDF2_NEWTON.M, BDF2 solver, using Newton's method;
• BE_NEWTON.M, backward Euler solver, using Newton's method;
• BE_PECE.M, backward Euler PeCe code;
• BUMP_ODE.M, y' = - y^2;
• MINUS_ODE.M, y' = - y;
• STIFF_ODE.M, a "stiff" ODE;
• STIFF_ODE_PARTIAL.M, more information about a "stiff" ODE;
• TRAPEZOID.M, trapezoid PeCeCe code;

Algorithm files for lab 6:

• DIF2.M, sets up the [1,-2,1] second difference matrix;
• KDV_MID.M, solves the KdV equation;
• KDV_MOVIE.M, animates the output of KDV_MID;
• METHOD_OF_LINES.M, a method of lines code for PDE's;
• SECANT.M, a secant method for use in shooting;

Algorithm files for lab 7:

• DETERMINANT.M, computes the determinant, the hard way;
• DIF2_INV.M, sets up the inverse second difference matrix;
• FRANK.M, sets up the Frank matrix;
• FRANK_INV.M, sets up the inverse Frank matrix;
• GE_CP.M, Gauss elimination, complete pivoting;
• GE_NP.M, Gauss elimination, no pivoting;
• GE_PP.M, Gauss elimination, partial pivoting;
• HILBERT.M, sets up the Hilbert matrix;
• HILBERT_INV.M, sets up the inverse Hilbert matrix;
• NEXT_PERM.M, returns the next permutation;
• PERM_SIGN.M, computes the sign of a permutation;

Algorithm files for lab 8:

• P_DET.M, computes the determinant of a permutation matrix;

Algorithm files for lab 9:

Algorithm files for lab 10:

• GRAM_SCHMIDT.M, carries out Gram-Schmidt orthgonalization of a set of vectors;
• HOUSEHOLDER.M, compute a Householder matrix used in constructing the QR factorization;
• RANDOM_ORTHOGONAL.M, returns a random orthogonal matrix;

Algorithm files for lab 11:

• JACOBI_DIF.M, the Jacobi iteration matrix for the difference matrix;
• LESP.M, returns a (full storage) Lesp tridiagonal matrix;
• MARKOV.M, the Markov matrix;
• RANDOM_TRI.M, returns a (full storage) random tridiagonal matrix;
• SEIDEL_DIF.M, the Gauss-Seidel iteration matrix for the difference matrix;
• SPLINE_TRI.M, returns a (full storage) tridiagonal matrix used in spline interpolation;
• TRI_DIF2.M, returns the compact difference tridiagonal matrix;
• TRI_FACTOR.M, factors a compact tridiagonal matrix;
• TRI_LESP.M, returns the compact Lesp tridiagonal matrix;
• TRI_RANDOM.M, returns a random compact tridiagonal matrix;
• TRI_SOLVE.M, solves a compact tridiagonal system;

Algorithm files for lab 12:

• EIGEN_TEST.M, several test matrices;