| LEC # | TOPICS | LECTURE NOTES |
|---|---|---|
| Ordinary Differential Equations | ||
| 1 | Numerical Integration of Ordinary Differential Equations: An Introduction | (PDF) drop_fe.m (M) drop_mp.m (M) drop_rhs.m (M) |
| 2 | Convergence and Accuracy | (PDF) ga_fe.m (M) ga_mp.m (M) |
| 3 | Convergence of Multi-Step Methods | (PDF) ga_ma2.m (M) |
| 4 | Systems of ODE's and Eigenvalue Stability | (PDF) fe_stab.m (M) nonpen_fe.m (M) nonpen_mp.m (M) |
| 5 | Stiffness and Implicit Methods | (PDF) dif1d.m (M) dif1d_fun.m (M) dif1d_main.m (M) eig_dif1d.m (M) mstepstab.m (M) stiff_err.m (M) stiff_forced.m (M) |
| 6 | Runge-Kutta Methods | (PDF) rkstab.m (M) |
| Finite Volume/Difference Methods | ||
| 7 | Conservation Laws and Finite Volume Methods | (PDF) convect1d.m (M) convect2d.m (M) |
| 8 | Finite Difference Methods for Convection-Diffusion | (PDF) convect1d_ftcs.m (M) |
| 9 | Matrix Stability Analysis | (PDF) condif1d_ftcs_eig.m (M) convect1d_ftcs_eig.m (M) |
| Midterm Exam | ||
| 10 | Fourier Stability Analysis | (PDF) |
| Finite Element Methods | ||
| 11 | Method of Weighted Residuals | (PDF) MWR_dif1d.m (M) |
| 12 | Finite Element Method for 1-D Diffusion | (PDF) fem_dif1d.m (M) fem_dif1d_gq.m (M) |
| 13 | Finite Element Method for 2-D Diffusion | (PDF) |
| 14 | Higher-order FEM | (PDF) fem1D_hier.m (M) fem1D_quad.m (M) |
| Probabilistic Methods | ||
| 15 | Introduction to Monte Carlo Method | (PDF) blade1D.m (M) bladedet.m (M) bladeLtbc.m (M) bladeuni.m (M) |
| 16 | Error Estimates for Monte Carlo Method | (PDF) |