Battery Differential Analysis

This repo contains two Matlab functions to compute the numerical differentiation of a vector.

Numerical differentiation of N uniformly spaced points implemented based on high-accuracy numerical differentiation formulas from [1].

dy = numDiff(y)

where:

• y is a column vector of uniformly spaced points of length N
• dy is the numerical derivative of y

Numerical differentiation of unevenly spaced points (non-equispaced data) implemented based on [1].

[dyNewton,dyLagrange] = numDiff2(xn,xm,ym)

where:

• xn is the query vector x of length N
• xm is the breakpoint (or knot) vector x of length M
• ym is the breakpoint (or knot) vector y of length M
• dyNewton is the derivative vector of length N computed using the piecewise constant approximation method (Newton)
• dyLagrange is the derivative vector of length N computed using the Lagrange interpolating polynomials method

Reference:

[1] Numerical Methods for Engineers Book by Raymond P. Canale and Steven C. Chapra.