MATLAB
Library


This library contains a catalogue of routines written in Matlab to perform a number of simple numerical procedures.
Click on the links to view each of the routines.

Number theory

  • harmonic: Summing the harmonic series
  • leibniz: Leibniz's series for pi
  • salamin: Gauss-Salamin algorithm

    Chaos

  • logistic: The logistic map
  • lorenz: The Lorenz equations

    Matrix methods

  • axbsolve: Gaussian elimination
  • gel: (echelon reduction function)
  • invert: invert a matrix
  • thomas: Thomas algorithm
  • jacobi: Jacobi iteration
  • seidel: Gauss-Seidel iteration
  • sorelax: Successive over-relaxtion

    Nonlinear equation solvers

  • bisect: Method of bisection
  • bisfun: (function required by bisect.m)
  • secant: Root finding using the secant method
  • itfun: (function required by secant)
  • newton: Root finding using Newton's method
  • itfun2: (function required by newton)
  • itfun2d: (function required by newton)

    Extrapolation and interpolation

  • aitken: Aitken extrapolation
  • poly: Polynomial interpolation
  • polyfit: (function required by poly)
  • vandermonde: Interpolating polynomial through solving the Vandermonde system

    Numerical Integration

  • trapez: The trapezium rule
  • fastrap: The trapezium rule (fast code)
  • simp: Simpson's rule (this code has been left incomplete deliberately)

    Numerical solution of ODEs

  • euler: Euler's method
  • crank: Crank-Nicolson method (example 1)
  • crank2: Crank-Nicolson method (example 2)
  • runge2: 2nd order Runge-Kutta integration
  • sysrung2.m: 2nd order Runge-Kutta integration for a system of ODEs
  • intfun: (function required by euler/runge2)
  • bvpex: To solve a boundary value problem

    Applications

  • blasius: Fluid flow over a wall
  • lotka2: The Lotka-Volterra equations (RK II)
  • lotka4: The Lotka-Volterra equations (RK IV)

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