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Numerical methods labs

Archived 2026 Author

Twelve lab programs for my numerical methods course, from nonlinear systems and linear solvers to finite-difference methods for partial differential equations.

Source
The heat equation and the Crank-Nicolson stencil on a chalkboard, with a plot of analytic against numerical solutions
Numerical methods labs · 2026

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  • Analytic solution against Crank-Nicolson (Jacobi and Thomas) and the explicit method
    Analytic solution against Crank-Nicolson (Jacobi and Thomas) and the explicit method
  • Runge's phenomenon, equidistant vs Chebyshev nodes
    Runge's phenomenon, equidistant vs Chebyshev nodes

Each lab is a small C++ program (several print their tables with my own hprint) with results plotted in Python. Among them: systems of nonlinear equations, Jacobi and other iterative solvers, Newton interpolation on equidistant and Chebyshev nodes (showing Runge's phenomenon), boundary value problems, explicit, implicit and trapezoidal time stepping with stability analysis, and Crank–Nicolson for the heat equation solved with both the Thomas algorithm and Jacobi iteration.