Chapter 1a and 1b

What are the characteristics of numerical methods?

• Dealing with large datasets or when iterative processes are involved, thus, save time and resources.

• Difficult to handle complex, nonlinear, and multidimensional mathematical problems.

• Suitable for real-world measurements and simulations.

Numerical methods consider and manage various types of errors, including round-off errors and truncation errors. What is round-off errors?

• Caused by finite precision in computer arithmetic

• Arising from approximations in the method

What is truncation errors?

• Caused by finite precision in computer arithmetic

• Arising from approximations in the method

Error analysis is crucial for assessing the accuracy of the results.

• Yes

• No

Common engineering applications that implement numerical method include assessing the stability and strength of structures (e.g.: off-shore platforms) under different loading conditions.

• Yes

• No

Several strategies to minimize errors in numerical methods are as below, EXCEPT :

• Reduce round-off errors by allowing more significant digits in calculations

• Use bigger time steps

• Choose appropriate algorithm

The effects of smaller time steps are :

• Reduce truncation error

• Lower accuracy

• Improve the convergence of the solution

• Require large and complex systems

Larger time steps reduce the computational load and speed up simulations.

• Yes

• No

The stopping error, sometimes called the "convergence criterion," determines when to terminate an iterative process. What criterion is used to decide if the current numerical solution is sufficiently accurate ?

• Ɛa > Ɛs

• Ɛa < Ɛs

Approximate error assess how close the numerical solution is to the true solution and guides the convergence process.

• Yes

• No