EP501 Example MATLAB Programs

Example codes, assignments, and exams for the EP 501 (numerical methods) course at Embry-Riddle Aeronautical University. This repository is a work in progress and will be updated as the semester progresses.

Codes updated for FA2020 semester

Basics of using matlab

1. located in ./matlab_basics/matlab_basics.m
2. illustrates precision, matrix operations, and plotting, along with some special functions

Numerical linear algebra

1. Located in ./linear_algebra/Ch1.m
2. Illustrates and checks various methods for solving matrix problems
3. contains functions for Gaussian elimination (Gauss_elim.m) and backsubstitution (backsub.m)
4. Contains examples of simple elimination (simple_elim_example.m) and Gaussian elimination (Gauss_elim_example.m)
5. Contains examples of iterative solutions to systems of equations (Jacobi_example.m)

Nonlinear equations

1. Located in ./nonlinear_eqns
2. Contains examples illustrating solutions of various nonlinear equations and systems
3. Contains examples of interval halving (interval_halving.m), false position (false_position.m), Newton's method for a single variable equation (Newton_Rhapson.m), and Newton's method for a 2D equation (Newton_Rhapson2D.m).
4. Contains various functions for exact Newton's method in 1D (newton_exact.m) and 2D (newton2D_exact.m)
5. Contains objective function which can be used as examples to demonstrate root finding algorithms (objfun*.m)

Polynomials and fitting

1. Located in ./polynomials
2. Contains examples of direct and approximate polynomial fits to data
3. Contains various examples of direct fitting (direct_fit.m), linear least squares (least_squares.m), and bilinear/spline interpolation (interpolation_examples.m).

Numerical differentiation and integration

1. located in ./differentiation
2. examples of finite difference formulas and applications
3. one-dimensional (derivative_examples.m) and multi-dimensional scripts (e.g. gradient operator, partial_derivative_examples.m)

Ordinary differential equations (ODEs)

1. located in ./ODEs
2. Examples of Methods for solving ordinary differential equations
3. Euler methods (Euler_methods.m), Runge-Kutta solutions (RK_methods.m), examples of resolving systems of ODEs (RK_systems.m), and backward difference formula comparisons (BDF_examples.m).

Partial differential equations (PDEs)

1. location in ./PDEs
2. Example solutions for elliptic (elliptic.m), parabolic (parabolic.m), and hyperbolic (hyperbolic.m) PDEs
3. Contains documentation describing analyitical solutions to test problems (./test_problems/)
4. Also contains various subroutines implementing BTCS for hyperbolic equations (BTCS_hyp.m), Lax-Friedrichs method (LaxFried.m), Lax-Wendroff (LaxWen.m), and Godunov's method (Godunov.m).
5. Advanced PDEs script (advanced_PDEs.m) is still under construction.