Numerical methods

Adams

Boundary value problem

Cubic spline

Discretization

Evaluation

Fehlberg

Gauss

Hexadecimal

Initial value problem

Junction

Knots

Least squares

Minimax

Non-automous

Ordinary differential equation

Pseudo-random numbers

Quasilinearization

Runge-Kutta

Shooting

Taylor series

Urabe

Variables

Wings

X-axis

Y-axis

Zero

Enter the appropriate term (from the above list) in the following blanks:

A __cubic spline___ can be used to approximate the value(s) of a function between a set of points (called __knots___) where the values of the function are known or given.

A famous numerical analyst named __________ developed special _________________ methods for solving differential equations. The methods allow for the estimation of the local truncation error.

A ___________________________ has a differential equation and a boundary condition.

The method of _____________________ can be used to approximate a set of noisy data such that the squares of the errors are minimized.

The _________ method is often the most efficient method for solving an ordinary differential equation subject to initial conditions when the derivatives are very expensive to evaluate and a fixed stepsize is a reasonable choice.

A _______________ method (for solving two-point boundary-value problems) is a method in which each iteration requires the solution of an initial value problem.

The E in the term PECE algorithm refers to an ___________________________________.

A Monte-Carlo simulation normally makes use of _____________________________________.

____ 13. Which of the following requires the solution of non-linear algebraic equations in order to

determine the coefficients of the method?

a. A high-order Runge-Kutta method

b. Adams-Bashforth-Adams-Moulton method

c. Taylor series method

d. An extrapolation method

_______ 14. Which of the following is most likely to suffer from numerical instability?

a. A tenth-order Runge-Kutta method

b. A tenth -order Adams-Bashforth-Adams-Moulton method

c. A tenth -order Taylor series method

d. Eulers method

________ 17. What is a shooting method?

a. An iterative method for approximating the solution of a two-point boundary value problem that makes use of a method for solving initial value problems

b. A direct method for solving initial value problems

c. A discretization method for solving a two-point boundary value problem

d. An iterative method for solving nonlinear algebraic equations

_______ 18. How could you start an Adams-Bashforth-Adams-Moulton method ?

a. Use a Taylor series method

b. Use a Runge-Kutta method

c. Either a or b

d. None of the above

_______ 19. When integrating an ordinary differential equation, if you take too small a stepsize,

a. rounding errors can dominate the solution

b. truncation errors will dominate the solution

c. numerical instability can cause problems

d. none of the above