function coefficients = central_difference(xs, x) ## ## The first order central difference at x1 is, ## ## f'(x1) = (f(x2) - f(x0))/2 ## ## where the index x1 is of course arbitrary but x2, x0 are adjacent ## to x1. The coefficients we seek are the coefficients of f(xj) for ## j = 1,...,N-2, where N is the length of ``xs``. We omit the first ## and last coefficient because at x0 and xN, the previous/next ## value is not available. ## ## This should probably take an 'order' parameter as well; see ## forward_euler(). ## ## INPUT: ## ## * ``xs`` - The vector of x-coordinates. ## ## * ``x`` - The point `x` at which you'd like to evaluate the ## derivative of the specified `integer_order`. This should be an ## element of `xs`. ## ## OUTPUT: ## ## * ``coefficients`` - The vector of coefficients, in order, of ## f(x0), f(x1), ..., f(xn). ## if (length(xs) < 3) ## We need at least one point other than the first and last. coefficients = NA; return; end x_idx = find(xs == x); if (x_idx == 1 || x_idx == length(xs)) ## You asked for the difference at the first or last element, which ## we can't do. coefficients = NA; return; end ## Start with a vector of zeros. coefficients = zeros(1, length(xs)); ## And fill in the two values that we know. coefficients(x_idx - 1) = -1/2; coefficients(x_idx + 1) = 1/2; end