Double Simpson Integration
Numerically evaluate double integral by 2-dimensional Simpson method.
simpson2d(f, xa, xb, ya, yb, nx = 128, ny = 128, ...)
f |
function of two variables, the integrand. |
xa, xb |
left and right endpoint for first variable. |
ya, yb |
left and right endpoint for second variable. |
nx, ny |
number of intervals in x- and y-direction. |
... |
additional parameters to be passed to the integrand. |
The 2D Simpson integrator has weights that are most easily determined by taking the outer product of the vector of weights for the 1D Simpson rule.
Numerical scalar, the value of the integral.
Copyright (c) 2008 W. Padden and Ch. Macaskill for Matlab code published under BSD License on MatlabCentral.
f1 <- function(x, y) x^2 + y^2 simpson2d(f1, -1, 1, -1, 1) # 2.666666667 , i.e. 8/3 . err = 0 f2 <- function(x, y) y*sin(x)+x*cos(y) simpson2d(f2, pi, 2*pi, 0, pi) # -9.869604401 , i.e. -pi^2, err = 2e-8 f3 <- function(x, y) sqrt((1 - (x^2 + y^2)) * (x^2 + y^2 <= 1)) simpson2d(f3, -1, 1, -1, 1) # 2.094393912 , i.e. 2/3*pi , err = 1e-6
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