Question

Use the modified Euler method to approximate the solutions to each of the following initial-value problems and compare the results to the actual values.

What method is used for the approximation in the given problem?
a. Modified Euler
b. Runge-Kutta
c. Newton's Method
d. Secant Method

Answer 1

The method used for the approximation in the given problem is the Modified Euler method, which is a numerical approximation technique used to solve ordinary differential equations.

Step-by-step explanation:

The method used for the approximation in the given problem is the Modified Euler method.

The Modified Euler method is a numerical approximation technique used to solve ordinary differential equations. It is an extension of the Euler method that offers better accuracy by taking into account the slope of the function at both the beginning and midpoint of the given interval.

To use the Modified Euler method, you need to follow these steps:

1. Calculate the increment value, h, by dividing the interval length by the desired number of steps.
2. Initialize the initial conditions (initial values) of the problem.
3. Iterate through each step of the interval, using the following formulas:
4. Repeat steps 3 and 4 for each step of the interval until the desired solution is obtained.
5. Compare the approximated solution to the actual values by calculating the absolute error or percentage error.