Spring 2008

R. J. Braun

Textbook functions

Interpolation functions

Pcwise linear interpolation: plinterp1.m

Hat function for interpolation: hatfun.m

Pcwise linear interpolation using hatfun.m: plinterp.m

Cubic spline interpolation without B-splines: spinterp1.m

B-spline creation: Bspline.m

Cubic spline interpolation using Bspline.m: spinterp.m

Global polynomial interpolation: polinterp.m

First kind Chebyshev weights and nodes: baryweightCheb1.m

Second kind Chebyshev weights and nodes: baryweightCheb2.m

Trigonometric interpolation: triginterp.m

Bezier curves: Bezier.m

Calculus functions

Finite difference formula weights: fdweights.m

Adaptive Simpson's method: adaptsimp.m

Clenshaw-Curtis Quadrature: ccquad.m

Gassian Quadrature: gquad.m

Clenshaw-Curtis Quadrature weights and nodes: clenshawcurtis.m

Gassian Quadrature weights and nodes: gauss.m

Double Exponential Quadrature: dequad.m

IVP functions

Euler's method: euler1.m

Euler's method for a system: eulersys.m

Improved Euler (RK2) method: ie2.m

RK4 method: rk4.m

RK23 method: rk23.m

AB4 multistep method: ab4.m

AM2 implicit method: am2.m

ABM4 predictor-corrector method: abm4.m

Scalar BD3 method: BD3scalar.m

BD3 method: BD3.m

BVP functions

Shooting method (Matlab 7): shoot.m shootexample.m

Shooting method (Matlab 6): shoot6.m

Linear finite difference method: fdlin.m

Nonlinear finite difference method: fdnonlin.m

PDE functions

Simple Euler method: heateq_expl3.m

Better Euler method function (Function 10.1): Eulerxx.m

Simple Backward Euler method: heateq_bkwd3.m

Better Backward Euler method function (Function 10.2): BExx.m

ode15s time stepping for heat equation (Function 10.4): ODE15x.m

ode45 time stepping for advection equation (Function 10.4): RK45x.m initfun.m

Leapfrog for advection equation with boundaries(unstable; Function 10.5): LFunxx.m icfun.m

Leapfrog for advection equation with boundaries(stable): LFxx.m

Poisson problem solution, general Dirichlet case: poissonfd.m

Poisson problem solution, homogeneous Dirichlet case: poissonfd2.m

Matlab example codes (not necessarily in text)

Cubic Spline Interpolation

Bspline creation: Bspline.m.

Bspline illustration: Bsplineexam1.m. Bsplineunity.m.

Not-a-Knot cubic spline function using B-spline: spinterp.m. Text example: Bsplineexam.m.

Lagrange Interpolation

Lagrange polynomial: LagrangeLs.m.

General weights for 2nd barycentric form interpolation: baryweight.m

2nd barycentric form interpolation: baryinterp.m

Interpolation and approximation

Runge phenomenon RungeEx1.m.

Fitting curve on Eiffel tower pic: EiffelFit2.m.

Eiffel photo Eiffel.jpg.

Two dimensional interpolation example: TwoDexample2.m.

Calculus

Maple file for computing 2nd derivative approximations (2nd order accurate): 2ndderiv.mw.

Midpoint rule with singular integrand, not good!: TryMidptSing.m.

Adaptive Simpson's rule: adaptsimp.m.

Compare Clenshaw-Curtis and Gauss-Legendre for a few functions: ExaCompCCG2.m.

Double exponential quadrature with singular integrand: TryDEQuad.m.

Initial Value Problems

Duffing oscillator (2nd order ode) script: ode_ex_duffing.m

Rossler equations (3rd order system) with external function: script: ode_ex_rossler.m ode function: rossler.m

Rossler equations (3rd order system) using single script: ode_ex_rossler2.m

Boundary Value Problems

Matlab bvp4c function on bvp from class notes: calling bvp4c: bvp_ex.m ode spec: bvp_exf.m bc spec: bvp_exbc.m

Allen-Cahn problem example of continuation. Script file to call bvp solver function: fdnl_cont.m Bvp solver fn: fdnl_gin.m Ode fn: allencahn.m.

Partial Differential Equations

Spectra from first and second derivative matrices: pseudospectrumHtAdv.m

Function for nonlinear pde with MOL and ode15s: ODE15_1d.m cahnallen1d.m.