A 4th order ODE can be written as this number of 1st order ODEs.
What is four?
100
ODEs that are very sensitive to step size in numerical solutions are classified as this.
What is conditionally stable?
100
This simple phrase would best describe the algorithm for Euler's Method.
What is New Value = Old Value + Slope x Step Size?
100
Numerical differentiation can be used in these two situations.
What are tabulated data or complicated functions?
200
ODEs that contain time as the independent variable are usually classified as this.
What is an Initial Value Problem?
200
ODEs that "blow up" regardless of step size in numerical solutions are classified as this.
What is ill-conditioned?
200
Euler's Method is really a truncation of this type of series expansion of a function.
What is a Taylor Series?
200
The O(hn) term at the end of a numerical differentiation formula represents this.
What is the truncation error?
300
A 13th order ODE initial value problem will require this number of initial conditions.
What is thirteen?
300
This is the basic mathematical structure of a 1st order ODE.
What is dy/dt = f(t,y); y(t=0)=y0?
300
This aspect of Euler's Method is of order O(h2).
What is the local truncation error?
300
Finite difference formulas for numerical differentiation are derived from this aspect of calculus.
What is the Taylor Series?
400
An ODE is classified as this if the dependent variable and its derivatives do not appear in products with themselves, raised to powers or in non - linear functions.
What is linear?
400
This aspect of Euler's Method is of order O(h).
What is the global truncation error?
400
Reducing the step size by 1/3 will do this to the truncation error in an O(h2) finite difference formula?
What is reduce the error by 1/9?
500
The mathematical equation that describes the motion of a simple mass-spring-damper system can be classified as this.
What is a 2nd order, linear, ODE?
500
This would be the main weakness of Euler's Method.
What is that the derivative at the beginning of the interval is assumed to apply across the entire interval?
500
If the tabulated data is not equally spaced, these are the only applicable finite-difference formulas.
What are the first-derivative forward and backward finite difference formulas?