CSC688/MTH686: Scientific Computation

Fundamentals

INTRO A few MATLAB examples including 2D and 3D graphics, animations, and matrix operations.

NUM2BIN Convert floating point number to binary string.

DOUBLE2BIN Convert double precision floating point number to binary string.

LONGHEX Long hexadecimal format for floating points less than one.

FLOATINGPOINTS Article by Cleve Moler on how IEEE Standard unifies arithmetic model.

POLYNOMIALS Solution to U. Kulisch polynomials puzzle.

Equation Solving

LOGISTIC Logistic map.

LOGMAPIT Iterations of the logistic map.

FIXEDPOINT Fixed point iteration.

NEWTON Root finding, Newton method.

NEWTONSYS Root finding, Newton method, systems of equations.

BISECTION Root finding, bisection method.

SECANT Root finding, secant method.

IQI Root finding, inverse quadratic interpolation method.

BIFDIAG Bifurcation diagram for logistic map.

ROOTS1 Roots of unity, basin of attraction.

CV Compares convergence rates for several root finding methods.

FROOT Simplified version of FZERO.

EQUATIONSOLVING Assignments.

EQUATIONSOLVING LaTeX source file for EQUATIONSOLVING.

ODEs

FP Forced pendulum (integration using the ODE family of solvers).

FP1EQ Forced pendulum equations (version 1).

FP2EQ Forced pendulum equations (version 2).

DUFF Conservative Duffing's oscillator (manifolds computation, comparison with finite-time and finite-scale Lyapunov exponents).

DUFF2EQ Conservative Duffing's oscillator equations.

ODE1 Solves ODEs using nonadaptive method of order 1 (Euler).

ODE2 Solves ODEs using nonadaptive method of order 2 (Heun).

ODE3 Solves ODEs using nonadaptive method of order 3 (Bogacki-Shampine).

ODE4 Solves ODEs using nonadaptive method of order 4 (classical Runge-Kutta).

ODE5 Solves ODEs using nonadaptive method of order 5 (Dormand-Prince).

IODE1 Solves ODEs using implicit nonadaptive method of order 1 (implicit Euler).

BVP Several boundary-valued problems.

SHOOT Solves boundary-valued second-order ODEs using a shooting method.

STURMLIOUVILLE The Sturm-Liouville eigenproblem.

PDEs

DIFFUSION1D Solves a 1D diffusion equation using forward-time difference, backward-time difference, and Crank-Nicolson methods.

DIFFUSION2D Solves a 2D diffusion equation using forward-time difference, backward-time difference, Crank-Nicolson, or Peaceman-Rachford method.

WAVE1D Solves a 1D wave equation using explicit and implicit methods.

WAVE2D Solves a 2D wave equation using explicit or implicit methods.

POISSON2D Solves a 2D Poisson equation with Dirichlet boundary conditions in rectangular domain using Gaussian elemination and fast sine transform methods.

PS2D 2D Poisson equation solver.

FPS2D Fast 2D Poisson equation solver.

HS2D 2D Helmholtz equation solver.

FHS2D Fast 2D Helmholtz equation solver.