SCPY 404/574 Numerical Methods for Differential Equations

Instructor	Chaiwoot Boonyasiriwat
Class Hours	Friday, 9.00AM - 12.00PM
Assessment	Homework 60%, Project 40%
Slides	01_ode.pdf 02_finite_difference.pdf 03_linear_solvers.pdf 04_fdtd.pdf 05_fdfd.pdf 06_finite_element.pdf 07_spectral_methods.pdf 08_ray_tracing.pdf 09_method_of_characteristics.pdf 10_finite_volume.pdf 11_cfd.pdf 12_neural_network.pdf
Online learning	Join

Tentative Course Schedule

Date	Topics	Videos	Assignments
Jan 14, 2022	Numerical methods for initial value problems Lab 1: Exponential decay problem: Comparison of Euler method and backward Euler method Codes: compare_euler_methods.m	View
Jan 21, 2022	Numerical methods for solving systems of linear algebraic equations Lab 2: Projectile motion with a linear drag: implementation of Euler, Heun, and RK4 methods	View	Submit HW1
Jan 28, 2022	Numerical methods for solving 2-point boundary value problems, finite-difference methods for elliptic PDEs	View
Feb 4, 2022	Symplectic Euler method, MATLAB ODE45 function, numerical methods for solving linear systems	View	Submit HW2
Feb 11, 2022	Finite-difference methods for solving parabolic and hyperbolic PDEs, finite-difference time-domain (FDTD) methods for linear wave simulation in the Cartesian coordinate system, numerical dispersion, von Neumann stability analysis, absorbing boundary conditions	View
Feb 18, 2022	FD for 2D Poisson equation, finite-difference frequency-domain (FDFD) methods	View
Feb 25, 2022	Finite-element methods: 1D boundary value problem, linear and nonlinear basis functions	Part 1, Part 2
Mar 11, 2022	Global and local descriptions, assembling global matrix, 1D diffusion problem	View
Mar 18, 2022	2D FEM, triangular and quadrilateral elements, MATLAB PDE Modeler	View	Submit HW3
Mar 25, 2022	Fourier spectral methods	View	Submit HW4
Apr 1, 2022	Chebyshev spectral methods, ray tracing, eikonal equation, upwind finite-difference method	View
Apr 8, 2022	Method of characteristics, finite volume method	View
Apr 22, 2022	Finite volume method (continued), computational fluid dynamics, Seibold (2008) (code)	View
Apr 29, 2022	Neural networks	View
May 6, 2022	Neural networks, CFD (continued)	View
May 20	Project presentation

References

Heath, M.T., 2002, Scientific Computing: An Introductory Survey, McGrawHill.
Hughes, T. J. R., 2000, The Finite Element Method: Linear Static and Dynamic Finite Element Analysis, Dover.
Inan, U. S., and R. A. Marshall, 2011, Numerical Electromagnetics: The FDTD Method, Cambridge University Press.
LeVeque, R. J., 2004, Finite Volume Methods for Hyperbolic Equation, Cambridge University Press.
LeVeque, R. J., 2007, Finite Difference Methods for Ordinary and Partial Differential Equation, SIAM.
Nocedal, J., and S. J. Wright, 2006, Numerical Optimization, Second Edition, Springer.
Trefethen, L. N. 2000, Spectral Methods in MATLAB, SIAM. (Companion website)
Versteeg, H. K., and W. Malalasekera, 2007, An Introduction to Computational Fluid Dynamics: The Finite Volume Method, Second Edition, Pearson Education.