solving ordinary differential equations fig the numerical solution at points can be extended by linear segments between the mesh points derive the differential equation model and then discretize it by numerical method is simply that the discretization can be done in many waysand we can create (muchmore accurate and more computationally efficient methods than ( or ( this can be useful in many problemsneverthelessthe forward euler scheme is intuitive and widely applicableat least when is chosen to be small the numerical solution between the mesh points our numerical method computes the unknown function at discrete mesh points tn what if we want to evaluate the numerical solution between the mesh pointsthe most natural choice is to assume linear variation between the mesh pointssee fig this is compatible with the fact that when we plot the array versus : straight line is drawn between the discrete points programming the forward euler schemethe special case let us compute ( in program the input variables are trand note that we need to compute new values total of values are needed in an array representation of our first version of this program is as simple as possiblen_ input('give initial population size n_ ' input('give net growth rate 'dt input('give time step size'n_t input('give number of steps'from numpy import linspacezeros linspace( (n_t+ )*dtn_t+ zeros(n_t+