Project 3 Numerical Methods for Differential Equations

Problem Set

The PDF below contains the specific problems for Project 3.

MATLAB Starter Files

To help you get started, incomplete MATLAB templates are provided. These files contain the structure, comments, and plotting code you must fill in the missing code where indicated by:

   = ;  % <-- COMPLETE: [description]

Each COMPLETE section includes a description of the mathematical formula you need to implement. All figures are saved automatically as .png files in your working directory.

Submission Instructions

Please submit the following two items on Canvas.

1. MATLAB Code (.m files)

Upload the following scripts and functions. Ensure your code is well-commented and runs without errors.

• Reusable Solver Functions:

• • fd_bvp_1d.m (1D BVP finite difference solver)
  • fd_poisson_2d.m (2D Poisson five-point stencil solver)

• Problem Scripts:

• • problem1_convergence.m(Problem 1 Grid refinement convergence study)
  • problem2_peclet.m (Problem 2 Central vs. upwind for convection-diffusion)
  • problem3_poisson.m (Problem 3 2D Poisson visualization and convergence)
  • problem4_iterative.m (Problem 4 Jacobi, Gauss-Seidel, and SOR comparison)

2. Written Report (PDF)

Submit a single PDF file (max 10 pages) containing:

• Figures: All plots generated by your MATLAB code with proper labels, titles, and legends (Blue sections).
• Tables: Convergence tables, iteration count tables, and solution range tables as specified.
• Critical Thinking: Written answers for Problems 1C, 2C, 3C, and 4C (Orange sections). Superficial answers will not receive full credit.

Recommended (not graded): Include a README.md describing each .m file and how to run the scripts. A template is provided in the starter files.

Grading

Problems 14: 25 points each (100 total). Points are distributed roughly equally between correct working code, properly formatted figures, and thoughtful Critical Thinking answers.

Struggling with your essay and deadlines?

Get this or a similar paper done in as fast as 4 hours, 24/7.

NB: We do not sell prewritten papers. All essays are written from scratch according to specific needs and instructions

✔Secure Service ✔ Plagiarism Free ✔On-time Delivery

WRITE MY PAPER