In the previous two problems, the error in the improved Euler method at $x = 0.1$ is
A) $0.00467$
B) 0.000165
C) 0.870
D) 0.895
E) 0.0897

Question

Quizplus · Accepted Answer

The improved Euler method, also known as Heun's method, is a numerical technique used to solve ordinary differential equations (ODEs). It provides a better approximation than the simple Euler method by taking the average of the slopes at the beginning and end of the interval. The error in numerical methods like this depends on the specific problem, step size, and the method's inherent accuracy. Among the options given, 0.000165 is a plausible small error value for the improved Euler method at $x = 0.1$, assuming a relatively small step size and a problem that is well-suited for this method. The other values are either too large to be typical errors for such a method at this point or do not fit the context of typical errors for an improved Euler method calculation.

In the Previous Two Problems, the Error in the Improved x=0.1x = 0.1x=0.1

In the Previous Two Problems, the Error in the Improved $x = 0.1$