atkinson

atkinson, an Octave code which contains examples from Atkinson's textbook "Elementary Numerical Analysis".

Licensing:

The information on this web page is distributed under the MIT license.

Languages:

atkinson is available in a Fortran77 version and a MATLAB version and an Octave version.

Related:

atkinson_test

cheney_kincaid, an Octave code which contains examples from Cheney and Kincaid's Numerical Mathematics and Computing text.

conte_deboor, an Octave code which contains examples from Conte and deBoor's Elementary Numerical Analysis text.

Author:

Original MATLAB version by Kendall Atkinson and Weimin Han.

Reference:

1. Kendall Atkinson, Weimin Han,
   Elementary Numerical Analysis,
   Wiley, 2004,
   ISBN: 0471433373,
   LC: QA297.A83.2004.

Source Code:

• ab2.m, use an Adams-Bashforth formula to solve a differential equation.
• bisect.m, use bisection to solve a nonlinear equation.
• deriv.m, evaluates the derivative for the direction field computation.
• dirfield.m, plots the direction field of y' = f(x,y).
• divdif.m, calculates a divided difference table.
• euler_back.m, uses the backward Euler method to solve an initial value problem.
• euler_for.m, uses the forward Euler method to solve an initial value problem.
• eulersys.m, uses Euler's method to solve a system of initial value problems.
• eval_exp_simple.m, evaluates several Taylor polynomials of increasing degree.
• eval_exp_tay.m, evaluates several Taylor polynomials of increasing degree.
• exp_tay.m, produces the Taylor coefficients for exp(x) around x=0.
• gaussint.m, estimates an integral using an n-point Gauss rule.
• gepivot.m, solves a system of linear equations using Gauss elimination with partial pivoting.
• gs.m, uses the Gauss-Seidel iterative method to solve a system of linear equations.
• heat1.m, uses the forward difference method to solve the initial boundary value problem of the heat equation.
• heat2.m, uses the backward difference method to solve the initial boundary value problem of the heat equation.
• humps_fun.m, evaluates the humps function, used for certain demonstrations.
• interp.m, evaluates an interpolant based on a divided difference table.
• jacobi.m, uses the Jacobi iterative method to solve a system of linear equations.
• log_tay.m, produces the Taylor coefficents of log(x) around x=1.
• ncs.m, compute the natural cubic spline interpolant to data.
• newton.m, uses Newton's method to solve a nonlinear equation.
• newton_sys.m, uses Newton's method to solve a system of nonlinear equations.
• odebvp.m, solves a two-point boundary value problem.
• plot_exp.m, plots several Taylor polynomials for exp(x).
• plot_log.m, plots several Taylor polynomials for log(x).
• plot_sin.m plots several Taylor polynomials for sin(x).
• plot_sint.m, plots several Taylor polynomials for the sine integral function.
• poisson.m, solves the Poisson problem on the unit square.
• polyeval.m, evaluates a Taylor polynomial.
• poly_even.m, evaluates an even Taylor polynomial.
• poly_odd.m, evaluates an odd Taylor polynomial.
• power_method.m, uses the power method to find the eigenvalue of largest magnitude associated with a matrix.
• secant.m, uses the secant method to solve a nonlinear equation.
• simpson.m, uses Simpson's rule to estimate the integral of a function.
• sin_tay.m, evaluates the coefficients of the Taylor approximation to the sine function.
• sint.m, evaluates an approximation to the sine integral function.
• sint_tay.m, evaluates the coefficients of the Taylor approximation to the sine integral function.
• taylor_3d.m, plots a 3D graph of variation in a Taylor approximation for log(x) of increasing degree.
• trapezoidal.m, uses the trapezoidal rule to estimate an integral.
• trapezoidal_ode.m, uses the trapezoidal rule to solve an initial value problem.
• tridiag.m, solves a tridiagonal system of linear equations.
• wave.m, uses centered differences to solve the initial-boundary value problem for the wave equation.