Abir Hasan Arko
← All projects

// C++

Numerical Computing Suite

  • shipped
  • 2024

C++ toolkit implementing 15+ classical numerical analysis algorithms: linear/non-linear solvers, interpolation, numerical differentiation/integration, curve fitting, ODEs (Newton-Raphson, Bisection, Simpson's rules, Runge-Kutta, LU decomposition).

  • C++
View source ↗

A from-scratch C++ implementation of the numerical methods I studied in my Numerical Methods course. The suite covers equation solving (Newton-Raphson, Bisection, Secant), interpolation (Newton forward/backward divided differences), numerical differentiation and integration (Simpson's 1/3 and 3/8, trapezoidal), curve fitting (least squares), ODEs (Runge-Kutta 4th order), and linear algebra (LU decomposition). Every method has a CLI demo with a known-good test case so you can compare numerical vs analytical results side by side.

Highlights

  • 15+ classical numerical methods with CLI demos and known-good test cases
  • Newton-Raphson, Bisection, Secant for non-linear equations
  • Simpson's 1/3, Simpson's 3/8, and trapezoidal rules for numerical integration
  • Runge-Kutta 4th order for ODEs and LU decomposition for linear systems

Challenges

  • Avoiding catastrophic cancellation in finite-difference formulas near singularities
  • Picking step sizes that balance truncation error vs round-off error in practice

What I learned

  • Numerical methods teach humility: small epsilon changes can flip convergence
  • Always print intermediate values — debugging numerics without them is guesswork

// more work

Other projects