mech0ctopus / numerical-analysis

Numerical analysis functions in MATLAB for interpolation, approximation, differentiation, integration, and solving systems of nonlinear equations.

numerical-analysis

Numerical analysis functions in MATLAB.

General Usage

From a file in the same directory as NumUtils.m call:

NumUtils.MethodName(args)

Methods

• AB2
  • Adams-Bashforth 2-step (AB2) LMM for solving IVP.
• Bisection
  • Bisection Method.
• CentralDiff
  • Central Difference for approximating f'(x0).
• EstimateFPIter
  • Estimates the number of iterations required for convergence of Fixed Point Iteration algorithm.
• EulersMethod
  • Euler's Method for solving an IVP.
• FivePointMidpoint
  • Five-Point Midpoint Formula for approximating f'(x0).
• FixedPointIter
  • Fixed Point Iteration.
• ForwardDiff
  • Forward Difference for approximating f'(x0).
• GaussSeidelMethod
  • Gauss-Seidel method for iteratively solving a linear system of equations.
• GramSchmidt
  • Construct orthogonal polynomials w/ Gram-Schmidt.
• Jacobian
  • Symbolically calculates Jacobian for a system.
• JacobisMethod
  • Jacobi's method for iteratively solving a linear system of equations
• Lagrange
  • Generate Lagrange interpolating polynomial.
• LLS
  • Constructs linear least squares polynomial coefficients
• LogB
  • Calculates log(X) with base B.
• NaturalCubicSpline
  • Calculates the natural cubic spline for f.
• NewtonsMethod
  • Newton's method for root finding problem
• NewtonsMethodForSystems
  • Newton's Method for iteratively solving a nonlinear system of equations F(x)=0.
• QuasiNewton
  • Quasi-Newton Method for root finding problem using global Bisection Method and local Newton's.
• QuasiSecant
  • Quasi-Secant Method for root finding problem using global Bisection Method and local Secant.
• RK2
  • Runge-Kutta 2-step (RK2) for solving IVP.
• SecantMethod
  • Secant method for root finding problem
• TaylorPoly
  • Symbolically calculate the first N terms of a Taylor Polynomial.
• TaylorPolyNTerm
  • Symbolically calculate the Nth term of a Taylor Polynomial.
• ThreePointEndpoint
  • Three-Point Endpoint Formula for approximating f'(x0).
• ThreePointMidpoint
  • Three-Point Midpoint Formula for approximating f'(x0).
• TruncationError
  • Symbolically calculate the truncation error associated with Taylor Polynomial approximation.
• TruncationErrorLagrange
  • Symbolically calculate the truncation error associated with Lagrange Interpolating Polynomial approximation.

References

• Numerical Analysis, 10th Edition by Burden, Faires, and Burden