Computational Methods with MATLAB Examples and Exercises

Computational methods exercises, examples, and solutions. The materials are commonly taught to mechanical engineering undergraduates.

King, Martin P., 2022, Computational Methods with MATLAB Examples and Exercises, [Book and Codes], doi: https://doi.org/10.5281/zenodo.6208040

Table of Contents

Foreword................................................................................................5

Exercise 1. 2D Laplace Equation (an elliptic PDE)................................7

Exercise 2. 2D Poisson Equation (an elliptic PDE)...............................11

Exercise 3. 1D Time-dependent Heat Conduction Equation (a parabolic PDE)....................15

Exercise 4. 2D Time-dependent Heat Conduction Equation (a parabolic PDE)....................18

Exercise 5. ODE – Numerical Order of Accuracy................................26

Exercise 6. ODE – Numerical Order of Accuracy and Stability...........30

Exercise 7. ODE – Lorenz Equations..................................................35

Exercise 8. ODE – Eigenvalues and Eigenvectors.............................41

Exercise 9. ODE – Boundary Value Problems...................................44

Exercise 10. Interpolation..................................................................47

Exercise 11. Filters............................................................................51

Bibliography........................................................................................56