1. How does the length of the time step (difference in time between successive steps) influence the accuracy of Euler's method?
A. Increasing the time step (larger steps) makes the solution more accurate
Incorrect. Increasing the time steps makes the solution less accurate
B. Increasing the time step (larger steps) makes the solution less accurate
Correct.
C. Increasing the time step (larger steps) does not change the solution
Incorrect. Numerical solutions are affected by the time-step length.
2. A differential equation has at least one term that contains the derivative of a variable (such as temperature, concentration, or velocity) with respect to another variable (such as time or distance). One example is: dx/dt = v where x is position, t is time, and v is velocity.
A. True
Correct.
B. False
Incorrect.
3. What does it mean to discretize a differential equation? (Select two correct answers)
A. It is the process of selecting specific points to seek a solution to an otherwise continuous problem.
Correct. Discrete time points are a sampling of values along a continuous range.
B. It gives an analytic (exact) solution to the differential equation once solved.
Incorrect. Numerical (discrete) solutions have calculation error that analytic solutions do not have.
C. Time steps are chosen to calculate a solution.
Correct. Numerical solutions require discretization where the solution is obtained at specific time points.