# ## Mathematica Lab Tutorials: Lab 11

### Lab Questions

Consider the following BVP With the boundary conditions and • Find the exact solution using the built-in DSolve function in Mathematica.
• Use the finite difference method with n=5 intervals to find a numerical solution.
• Plot the exact solution overlapping the data points obtained using the numerical solution.
• Find the maximum absolute error.
• Write a procedure whose input is and the output is the maximum absolute error.
• Plot the curve of the maximum absolute error vs. for • Plot the curve of the maximum absolute error vs. for • Fit the nonlinear model to the data of maximum error vs. (Note the error is expected to be because the basic formula for the centred finite difference scheme is used)

### Video Tutorials

#### Tutorial 1

Finding exact solutions using DSolve function. A review of FullSimplify and Solve functions. Introducing the Symbol function.

#### Tutorial 2

Using the finite difference method to solve differential equations.

#### Tutorial 3

An example of finding the error in the finite difference method as a function of the number of intervals.