Chebfun Examples listing
Here is the complete list of Chebfun Examples and the sections they belong to.
integro
| (html, PDF, M-file) | ||
| Absolute value approximations by rationals | approx | (html, PDF, M-file) |
| Absolute value approximations by rationals 2 | approx | (html, PDF, M-file) |
| Adding Together Bump Functions | approx | (html, PDF, M-file) |
| Advection-diffusion equation with a jump | ode | (html, PDF, M-file) |
| An Allen-Cahn equation with continuation | ode | (html, PDF, M-file) |
| Analytic continuation via rational approximation | complex | (html, PDF, M-file) |
| ANGLE, UNWRAP, and branches of complex chebfuns | complex | (html, PDF, M-file) |
| Approximation of piecewise linear functions (& chebsnake!) | fun | (html, PDF, M-file) |
| Arc length in the complex plane | complex | (html, PDF, M-file) |
| Area and centroid of a 2D region | geom | (html, PDF, M-file) |
| Automatic differentiation in Chebfun | ode | (html, PDF, M-file) |
| B-splines and convolution | approx | (html, PDF, M-file) |
| Battery test of Chebfun as an integrator | quad | (html, PDF, M-file) |
| Bernstein polynomials | approx | (html, PDF, M-file) |
| Best approximation with the Remez command | approx | (html, PDF, M-file) |
| Birthday cards and analytic functions | fun | (html, PDF, M-file) |
| The Birthday Paradox | fun | (html, PDF, M-file) |
| The Bivariate Normal Distribution | stats | (html, PDF, M-file) |
| BLOODHOUND Supersonic Car | ode | (html, PDF, M-file) |
| Blowup equation (Frank-Kamenetskii) | ode | (html, PDF, M-file) |
| A Bouncing Ball | ode | (html, PDF, M-file) |
| Bouncing photon, Sinai billiards | geom | (html, PDF, M-file) |
| Boundary layer for advection-diffusion equation | ode | (html, PDF, M-file) |
| Can one hear the shape of a chebfun? | fun | (html, PDF, M-file) |
| Carrier equation | ode | (html, PDF, M-file) |
| Central Limit Theorem | stats | (html, PDF, M-file) |
| Chebyshev coefficients | approx | (html, PDF, M-file) |
| Chebyshev interpolation of oscillatory entire functions | approx | (html, PDF, M-file) |
| Chebyshev polynomials as plotted by Higham and Higham | approx | (html, PDF, M-file) |
| Checking vector calculus | veccalc | (html, PDF, M-file) |
| Classification of linear dynamical systems | veccalc | (html, PDF, M-file) |
| Complex roots near the real axis | roots | (html, PDF, M-file) |
| Computing common roots of two bivariate functions | roots | (html, PDF, M-file) |
| Condition numbers of various bases | linalg | (html, PDF, M-file) |
| Conformal map to a square | complex | (html, PDF, M-file) |
| Convergence rates for interpolating functions | approx | (html, PDF, M-file) |
| Coupled system of reaction-diffusion equations | pde | (html, PDF, M-file) |
| Dawson's integral | ode | (html, PDF, M-file) |
| Definite and Indefinite Integrals | calc | (html, PDF, M-file) |
| Delta and Heaviside Hyperfunctions | complex | (html, PDF, M-file) |
| Delta functions and derivatives | calc | (html, PDF, M-file) |
| Delta Functions and ODEs | ode | (html, PDF, M-file) |
| The Dixon-Szego function in 2D optimisation | opt | (html, PDF, M-file) |
| Double-well Schrödinger eigenstates | ode-eig | (html, PDF, M-file) |
| Dual points, lines, polygons and curves | geom | (html, PDF, M-file) |
| Eigenstates of the Schrödinger equation | ode-eig | (html, PDF, M-file) |
| Eigenvalue level repulsion | linalg | (html, PDF, M-file) |
| Eigenvalues of the Fox-Li integral operator | integro | (html, PDF, M-file) |
| An ellipse rolling around another ellipse | geom | (html, PDF, M-file) |
| Encryption of a message with SCRIBBLE | fun | (html, PDF, M-file) |
| Exact Chebyshev expansion coefficients of a function | approx | (html, PDF, M-file) |
| Exact solutions of some ODEs | ode | (html, PDF, M-file) |
| Exponential Distribution -- Exercises from a Textbook | stats | (html, PDF, M-file) |
| Extrema of a complicated function | opt | (html, PDF, M-file) |
| The FFT in Chebfun | approx | (html, PDF, M-file) |
| Field of values and numerical abscissa | linalg | (html, PDF, M-file) |
| First example with Chebop2 | pde | (html, PDF, M-file) |
| Fractional calculus in Chebfun | integro | (html, PDF, M-file) |
| Frequencies of a drum | ode-eig | (html, PDF, M-file) |
| The gamma function and its poles | approx | (html, PDF, M-file) |
| Gauss and Clenshaw-Curtis quadrature | quad | (html, PDF, M-file) |
| Gauss quadrature nodes and weights | quad | (html, PDF, M-file) |
| Generalized polynomial chaos | stats | (html, PDF, M-file) |
| The global minimum of a complicated function | opt | (html, PDF, M-file) |
| Gravitational force between two cubes | quad | (html, PDF, M-file) |
| A greedy algorithm for choosing interpolation points | approx | (html, PDF, M-file) |
| Half-wave rectifier | ode | (html, PDF, M-file) |
| Halphen's constant for approximation of exp(x) | approx | (html, PDF, M-file) |
| Happy Valentines Day! | fun | (html, PDF, M-file) |
| Happy Valentines Day! (again) | fun | (html, PDF, M-file) |
| Heat equation via EXPM | pde | (html, PDF, M-file) |
| Hello World | fun | (html, PDF, M-file) |
| A Hilbert curve on a surface and Chebsnake2 | fun | (html, PDF, M-file) |
| Histogram from function or data | stats | (html, PDF, M-file) |
| Illustrating the mathematics of signal processing in Chebfun | approx | (html, PDF, M-file) |
| Implicit functions and fun with contours | fun | (html, PDF, M-file) |
| Interactive Interpolation | approx | (html, PDF, M-file) |
| Jump Conditions in BVPS | ode | (html, PDF, M-file) |
| A keyhole contour integral | complex | (html, PDF, M-file) |
| Koch Snowflake | fun | (html, PDF, M-file) |
| Lane-Emden equation from astrophysics | ode | (html, PDF, M-file) |
| Least-squares data fitting and POLYFIT | stats | (html, PDF, M-file) |
| Lebesgue functions and Lebesgue constants | approx | (html, PDF, M-file) |
| Lee and Greengard ODE examples | ode | (html, PDF, M-file) |
| Linear EXP initial-value problem | ode | (html, PDF, M-file) |
| Linear sine/cosine initial-value problem | ode | (html, PDF, M-file) |
| Lissajous curves | geom | (html, PDF, M-file) |
| Local complexity of a function | approx | (html, PDF, M-file) |
| Lorenz Attractor in the Complex Plane using RATINTERP | ode | (html, PDF, M-file) |
| Marching Squares | roots | (html, PDF, M-file) |
| Matched asymptotics and boundary layers | ode | (html, PDF, M-file) |
| MathJax introduction | fun | (html, PDF, M-file) |
| Maxwell's equations | pde | (html, PDF, M-file) |
| Mean Value Theorem | calc | (html, PDF, M-file) |
| Mercer's theorem and the Karhunen-Loeve expansion | stats | (html, PDF, M-file) |
| Mercury-Earth Conjunctions | linalg | (html, PDF, M-file) |
| Mercury-Earth minimum separation | opt | (html, PDF, M-file) |
| Merry Christmas! | fun | (html, PDF, M-file) |
| Model of a quantum dot array for solar energy | ode-eig | (html, PDF, M-file) |
| Multiple BVP solutions by solving an IVP | ode | (html, PDF, M-file) |
| The mystery of Bernoulli polynomials | roots | (html, PDF, M-file) |
| A new bivariate rootfinder based on Bezout resultants | roots | (html, PDF, M-file) |
| Newton's Method | roots | (html, PDF, M-file) |
| Nonlinear ODE modeling solar magnetic fields | ode | (html, PDF, M-file) |
| Nonnormality quiz from Trefethen and Embree | linalg | (html, PDF, M-file) |
| Nonstandard 'boundary' conditions | ode | (html, PDF, M-file) |
| Normal Distribution -- Exercises from a Textbook | stats | (html, PDF, M-file) |
| The nullspace of a linear operator | ode-eig | (html, PDF, M-file) |
| Optimal bet-sizing and the Kelly Criterion | stats | (html, PDF, M-file) |
| Optimization of a parameterised integral | opt | (html, PDF, M-file) |
| Optimizing a bird's flight path | calc | (html, PDF, M-file) |
| Orbiting around fixed stars | ode | (html, PDF, M-file) |
| Orr-Sommerfeld eigenvalues | ode-eig | (html, PDF, M-file) |
| Orthogonal polynomials via the Gram-Schmidt process | approx | (html, PDF, M-file) |
| Orthogonal polynomials via the Lanczos process | approx | (html, PDF, M-file) |
| An oscillatory integral | quad | (html, PDF, M-file) |
| A parameter dependent ODE with breakpoints | ode | (html, PDF, M-file) |
| Parameter-dependent ODEs: Three examples | ode | (html, PDF, M-file) |
| Parametric Surfaces | geom | (html, PDF, M-file) |
| Perimeter of an ellipse | geom | (html, PDF, M-file) |
| A periodic ODE system | ode | (html, PDF, M-file) |
| Phase Portrait Plots | complex | (html, PDF, M-file) |
| Phase Portraits | complex | (html, PDF, M-file) |
| Phase portraits and trajectories | veccalc | (html, PDF, M-file) |
| Phase Portraits for Functions with Poles | complex | (html, PDF, M-file) |
| Piecewise operators demo | ode | (html, PDF, M-file) |
| Polynomial basis for Hermite interpolation | approx | (html, PDF, M-file) |
| Polynomial eigenproblems with differential operators | ode-eig | (html, PDF, M-file) |
| Pretty functions approximated by Chebfun2 | approx | (html, PDF, M-file) |
| Procrustes shape analysis | geom | (html, PDF, M-file) |
| Quadrature convergence rates for differentiable functions | quad | (html, PDF, M-file) |
| Rational approximation to the exponential in a complex region | approx | (html, PDF, M-file) |
| Rational interpolation, robust and non-robust | approx | (html, PDF, M-file) |
| Resolvent norm on the imaginary axis | linalg | (html, PDF, M-file) |
| Resonance exploited by Carrier and Pearson's vandal | ode | (html, PDF, M-file) |
| Restricted-denominator approximations | approx | (html, PDF, M-file) |
| Roots of a Bessel function | roots | (html, PDF, M-file) |
| Roots of a complex function via Cauchy integrals | roots | (html, PDF, M-file) |
| Roots of a secular equation with poles | roots | (html, PDF, M-file) |
| Roots of random polynomials | roots | (html, PDF, M-file) |
| The Rosenbrock function in 2D optimisation | opt | (html, PDF, M-file) |
| The Rosenbrock function in 2D optimisation (revisited) | opt | (html, PDF, M-file) |
| Rouche's Theorem | complex | (html, PDF, M-file) |
| Rounding Corners by Convolution | geom | (html, PDF, M-file) |
| Sampling from a Probability Distribution | stats | (html, PDF, M-file) |
| Schwarz-Christoffel toolbox and Chebfun | complex | (html, PDF, M-file) |
| Simple computations with probability distributions | stats | (html, PDF, M-file) |
| Singular value decomposition of compact operators | pde | (html, PDF, M-file) |
| Spectral radius of the SOR iteration matrix | linalg | (html, PDF, M-file) |
| Spike integral | quad | (html, PDF, M-file) |
| Splines | approx | (html, PDF, M-file) |
| Stability of a thermoelastic rod | ode-eig | (html, PDF, M-file) |
| Stability regions of ODE formulas | ode | (html, PDF, M-file) |
| Stochastic collocation for Burgers' equation | stats | (html, PDF, M-file) |
| Summing a divergent Series | approx | (html, PDF, M-file) |
| Surfaces of revolution | calc | (html, PDF, M-file) |
| System of two nonlinear BVPs | ode | (html, PDF, M-file) |
| Three body problem complex singularities | ode | (html, PDF, M-file) |
| Time independent Black-Scholes with jumps | ode | (html, PDF, M-file) |
| Time-dependent integro-differential equation | pde | (html, PDF, M-file) |
| Time-independent Schrödinger eqn & reflection coefficients | ode | (html, PDF, M-file) |
| Transient Growth | linalg | (html, PDF, M-file) |
| Undergraduate Multivariable Calculus | veccalc | (html, PDF, M-file) |
| The Volume of a Heart and the Divergence Theorem | geom | (html, PDF, M-file) |
| Wave equation with decay band | ode-eig | (html, PDF, M-file) |
| The white curves of Ortiz and Rivlin | roots | (html, PDF, M-file) |
| A wiggly function and its best approximations | approx | (html, PDF, M-file) |
| Wikipedia integro-differential equation example | integro | (html, PDF, M-file) |
| Wikipedia ODE examples | ode | (html, PDF, M-file) |
| Writing a message in 3D | fun | (html, PDF, M-file) |