17.14. Numerical Solution Techniques

Try these first

1. 1.

   What does the Finite Difference Method (FDM) do?

   Hint

   Think about how it transforms a differential equation into manageable parts.

2. 2.

   What is the main advantage of numerical methods?

   Hint

   No hint provided

3. 3.

   What does the Finite Difference Method (FDM) approximate?

   • Time only
   • Space only
   • Both space and time

   Hint

   Remember that FDM deals with both dimensions.

4. 4.

   Is the Finite Element Method suitable for complex geometries?

   • True
   • False

   Hint

   Think about the capability of FEM discussed in class.

5. 5.

   Using the Finite Difference Method, derive the iterative formula to approximate the wave equation on a string of length L and tension T. Assume small displacements and use a grid of 10 segments.

   Hint

   Think about how the grid influences your calculations based on previous steps.

6. 6.

   Evaluate a structure using FEM. Consider a beam with varying cross-section under a static load. Discuss how you would set up the problem including nodes and elements.

   Hint

   Make sure to think about where each change occurs in the structure to set the elements effectively.