Page - 214 - in Programming for Computations – Python - A Gentle Introduction to Numerical Simulations with Python 3.6, Volume Second Edition

214 8 SolvingOrdinaryDifferentialEquations Fig. 8.3 Mesh in timewithcorresponding discrete values (unknowns) Fig. 8.4 Illustration of a forward difference approximation to the derivative The collection of points t0,t1,.. .,tNt is called a mesh (or grid), while the correspondingun values4 collectivelyare referred to asamesh function. Let us use an example to illustrate the givensteps. First, we introduce the mesh, which often is uniform, meaning that the spacing between mesh points tn and tn+1 4 To get an estimate of u in between the mesh points, one often assumes a straight line relationship between computed un values. Check out linear interpolation, e.g., on Wikipedia (https://en.wikipedia.org/wiki/Linear_interpolation).