In the previous two problems, the error in the improved Euler method at $x = 0.1$ is
A) 0.00467
B) 0.000168
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 step size and the nature of the differential equation being solved. Among the given options, 0.000168 is a plausible error magnitude for the improved Euler method at $x = 0.1$, considering it generally yields more accurate results than the basic Euler method, which often has larger errors. The exact error value can be determined by comparing the numerical solution to the exact solution of the ODE at $x = 0.1$, but without the specific ODE and step size, we rely on the typical accuracy improvement of the improved Euler method for this answer.

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 $x = 0.1$