Introduction to Scientific Computing : Lecture 27 codes

Ballistics example

Computational routines

• fball.m -- right hand side for an ODE for the ballistics problem with drag.
• hitground.m -- event function to indicate when a projectile hit the ground.
• ftarget.m -- evaluate the impact distance for different targeting angles.
• find_anglec.m -- do root-finding on a Chebyshev interpolant to compute angles for hitting a target at a specified distance.

Demo drivers

• balldefault.m -- set up default physical parameters for an example ballistics problem.
• testball1.m -- basic sanity check of the ballistics ODE right-hand side function.
• testball2.m -- basic check of the use of the Events option in ode45.
• testball3.m -- check the accuracy of low-order Chebyshev interpolation to estimate the angle-distance curve.
• testball4.m -- check the computation of targeting angles via Chebyshev interpolation of the angle-distance curve.

Particle-in-box example

Computational routines

• particlebox.m -- compute the first four energy levels for the "particle in a box" model using second-order finite differences.
• particleboxc.m -- compute the first four energy levels for the "particle in a box" model using a Chebyshev collocation scheme.

Demo drivers

• particlebox_cvg.m -- illustrate the convergence of the energy levels for the "particle in a box" model using second-order finite differences.
• particleboxc_cvg.m -- illustrate the convergence of the energy levels for the "particle in a box" model using Chebyshev collocation.

Support routines

• cheb.m -- compute Chebyshev points and differentiation matrix
• chebeval.m -- evaluate a Chebyshev interpolant by barycentric interpolation. See Trefethen's Approximation Theory and Approximation Practice for details.
• chebopt.m -- find local maxima of a Chebyshev interpolant via a not-very-smart Newton iteration