Solving Nonlinear Equations with Newton's Method

Software collection

• MATLAB.tar.gz a tarball of the whole thing
• The solvers for systems of equations:
  • nsold.m Newton's method, direct factorization of Jacobians
  • nsoli.m Newton-Krylov methods, no matrix storage
  • brsola.m Broyden's method, no matrix storage
    
• Chapter 1: Introduction
  • Solvers: newtsol.m , secant.m , chordsol.m
  • Examples:
    • tan(x) - x = 0: tandemo.m , ftan.m
    • atan(x) = 0: ataneg.m
• Chapter 2: Finding the Newton Step with Gaussian Elimination using nsold.m
  • atan(x) = 0: fatan.m , atandemo.m
  • Simple 2-D problem: simple.m , simpdemo.m
  • H-equation: heq.m , heqdemo.m .
  • Two-point boundary value problem: bvpsys.m , bvp2demo.m .
  • Time dependent initial-boundary value problem: timedep.m , ftime.m
    
• Chapter 3: Newton-Krylov Methods using nsoli.m
  • H-equation: heq.m , heqkdemo.m .
  • OZ-equations: oz.m , ozdemo.m , ozmovie.m .
  • PDE Examples:
    Left precondtioning: pdeleft.m , pdeldemo.m
    Right precondtioning: pderight.m , pderdemo.m
    Time dependent PDE in 2D: pdetime.m , pdetimedemo.m .
  • Poission Solver Preconditioner: fish2d.m
  • Matrix-free derivatives: dxmf.m , dymf.m , lapmf.m
    
• Chapter 4: Broyden's Method using brsola.m
  • H-equation: heq.m , heqbdemo.m . heqmovie.m .
  • PDE Examples; Compare Newton-Krylov to Broyden's method:
    Left precondtioning: pdeleft.m , pdebrl.m
    Right precondtioning: pderight.m , pdebrr.m
  • Poission Solver Preconditioner: fish2d.m
  • Matrix-free derivatives: dxmf.m , dymf.m , lapmf.m

last changed 1/31/06 dar