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Mathematics Final Year Topic: Convergence of Jacobi and Gauss–Seidel Iteration for a Discretised Poisson Problem

This Mathematics final year project compares stationary iterations on matrices arising from a fixed boundary-value discretisation.

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Why choose this project topic?

A focused study of poisson iteration gives you a specific question in numerical linear algebra. It compares stationary iterations on matrices arising from a fixed boundary-value discretisation. The bounded comparison creates room to explain how your evidence supports an interpretation and where the method has limits.

How does grid refinement influence the convergence of Jacobi and Gauss–Seidel methods for a selected Poisson system?

Agree the apparatus or dataset, comparison range and feasible measurement schedule for poisson iteration with your supervisor.

Proposed project objectives

  1. 01Define the materials, variables and comparison conditions for poisson iteration.
  2. 02Construct the system from a stated domain and boundary treatment.
  3. 03Evaluate the measurements or model outputs in relation to this question: How does grid refinement influence the convergence of Jacobi and Gauss–Seidel methods for a selected Poisson system?

A suggested research approach

Construct the system from a stated domain and boundary treatment. Analyse iteration matrices where feasible, compare residual and solution-error histories and use the same initial guess and stopping definitions across methods. Agree the available resources and record uncertainty, deviations from the protocol and any observations that challenge the initial interpretation.

What you will need

  • A defined Poisson boundary-value problem
  • Matrix and iteration-matrix construction tools
  • A validated reference solution and stopping rules

Keep your project scope clear

Residual reduction is not identical to forward-error reduction, especially when the system becomes more ill-conditioned.

Mathematics project chapter outline

Use this outline as a starting point. You can edit the chapter titles to match your department’s format during setup.

  1. Chapter 1Introduction
  2. Chapter 2Literature Review
  3. Chapter 3Theory and Methodology
  4. Chapter 4Results and Applications
  5. Chapter 5Summary, Conclusion and Recommendations

Turn this topic into your own final year project.

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