Euler's Method and Error Analysis

The video tutorial explains how to approximate the value of a function using Euler's method. It begins with setting up the problem and explaining the method's application when solving differential equations analytically is difficult. The tutorial provides a step-by-step calculation of the approximation for y(1) using a step size of 0.25. It concludes with a comparison of the approximation to the actual value, calculating the absolute and relative errors, and discussing the acceptability of the approximation.

What is the initial condition given in the problem?

• y(0) = 1

• y(1) = 0

• y(0) = 0

• y(1) = 1

What is the purpose of using Euler's method in this context?

• To approximate solutions to differential equations

• To calculate integrals

• To solve algebraic equations

• To find the exact solution to differential equations

What is the step size (h) used in Euler's method for this problem?

• 1.0

• 0.5

• 0.25

• 0.1

How is the value of y1 calculated in Euler's method?

• y0 / h * f(x0, y0)

• y0 * h * f(x0, y0)

• y0 - h * f(x0, y0)

• y0 + h * f(x0, y0)

What is the approximate value of y2 calculated using Euler's method?

• 1.0156

• 1.0000

• 1.0791

• 1.2308

What is the final approximation of y(1) using Euler's method?

• 1.3956

• 1.0156

• 1.2308

• 1.0791

What is the actual value of y(1) according to the particular solution?

• 1.3956

• 1.2308

• 1.0791

• 1.0156

How is the absolute error calculated?

• Difference between the true value and the approximation

• Sum of the true value and the approximation

• Product of the true value and the approximation

• Ratio of the true value to the approximation

What is the relative error expressed as a percentage?

• 12.23%

• 10.23%

• 8.23%

• 5.23%

Is the approximation acceptable if up to 10% error is allowed?

• No, it is not acceptable

• Yes, it is acceptable

• It depends on the context

• The error percentage is not given