Lecture schedule
Note: This schedule is subject to revision during the term.
Monday, April 2
Finite difference formulas for approximate differentiation [5.1.1].
Wednesday, April 4
Rounding error [5.1.2]. Simple Matlab programs (functions) for numerical differentiation:
 Twopoint forward difference formula: d1fd2p.m
 Threepoint centereddifference formula: d1cd3p.m
 Twopoint forward difference formula, varying h: d1fd2p_varh
 Threepoint centereddifference formula, varying h: d1cd3p_varh.m
Friday, April 6
Extrapolation [5.1.3]. About symbolic differentiation and integration [5.1.4]. Trapezoid rule [5.2.1].
Monday, April 9
NewtonCotes formulas [5.2]: Trapezoid, Midpoint, Simpson's rules, Open or Composite formulas.
Wednesday, April 11
NewtonCotes formulas [5.2]: Order of approximation, degree of precision, Newton's (or Simpson's 3/8) and Boole's rules, higher order open rules.
Friday, April 13
A posteriori error estimates and stopping criteria. Romberg integration [5.3].
Monday, April 16
Adaptive quadrature [5.4].
 Adaptive trapezoid method (uses trap.m above): adaptrap.m
Wednesday, April 18
GaussLegendre quadrature [5.5].
Friday, April 20
Initial value problems [6.1]. Existence and uniqueness [6.1.2]. Euler's method [6.1.1].
Monday, April 23
Analysis of initial value problem solvers [6.2]. Local and global truncation error [6.2.1]. Continuous dependence on initial condition [6.1.2]. The explicit trapezoid (or Heun's) method [6.2.2]. The midpoint method [6.4.1].
Wednesday, April 25
Local truncation error of the (Heun's) explicit trapezoid method [6.2.2]. Taylor methods [6.2.3].
Friday, April 27
Systems of ordinary differential equations [6.3]. Higher order equations [6.3.1]. The physical pendulum [6.3.2].
 Euler's method for vector equations: euler.m
 Heun's method for vector equations: heun.m
 The midpoint method for vector equations: midpoint.m
 Pendulum program from the textbook had a bug, which is fixed by Matt Comber here: pend.m
Monday, April 30
Orbital mechanics [6.3.3]. Computer demo.
 The onebody program is modified to simulate twobody problem: orbit2.m
Wednesday, May 2
RungeKutta methods [6.4]. The HodgkinHuxley neuron [6.4.2].
 RungeKutta method of order 4: rk4.m
Friday, May 4
The Lorenz equations [6.4.3]. Computer demo.
Monday, May 7
Variable stepsize (aka adaptive) methods [6.5]: Embedded RungeKutta pairs [6.5.1].
 RungeKuttaFehlberg order 4 / order 5 embedded pair: rkf45.m
Wednesday, May 9
Review.
Friday, May 11
Midterm exam.
Monday, May 14
Implicit methods and stiff equations [6.6]: Backward Euler method.
 Backward Euler with Newton's method as a solver: beuler.m
 A simple implementation of Newton's method: newton.m
Wednesday, May 16
Multistep methods [6.7]: AdamsBashforth methods [6.7.2], AdamsMoulton methods [6.7.3], predictorcorrector methods [6.7.3].
 AdamsBashforth 4step method: ab4.m
 AdamsBashforth / AdamsMoulton predictorcorrector pair of order 4: abm4.m
Friday, May 18
Analysis of multistep methods [6.7]: Stability, consistency, and convergence. Dahlquist's theorem. General linear twostep methods.
Monday, May 21
Boundary value problems [7.1.1]. Linear shooting method. General shooting method [7.1.2].
 Shooting method for linear 2nd order Dirichlet BVPs (with fixed stepsize IVP solvers): linshoot.m
 Shooting method using bisection for 2nd order Dirichlet BVPs (with fixed stepsize IVP solvers): bisectshoot.m
 Shooting method using bisection for 2nd order Dirichlet BVPs (with RungeKuttaFehlberg 4/5 variable stepsize solver): rkf45bisectshoot.m
Wednesday, May 23
Finite difference methods for linear boundary value problems [7.2.1].
 FD method for linear 2nd order Dirichlet BVPs: linfd.m
Friday, May 25
FD methods for nonlinear BVPs [7.2.2].
 FD method for nonlinear 2nd order Dirichlet BVPs (using a fixed point iteration): fpifd.m
 FD method for nonlinear 2nd order Dirichlet BVPs (using Newton's iteration): newtfd.m
Monday, May 28
Memorial Day.
Wednesday, May 30
Collocation method [7.3.1].
Friday, June 1
Collocation method [7.3.1].
Monday, June 4
Galerkin method. Finite elements [7.3.2].
Wednesday, June 6
Galerkin method. Finite elements [7.3.2].
Friday, June 8
Review.
Friday, June 15
Final exam. Time: 11:30am2:29pm. Place: HSS1315.
