instead of going to the limit we can use small twhich yields computable approximation to tn / tn unc un this is known as forward difference since we go forward in time (unc to collect information in to estimate the derivative figure illustrates the idea the error of the forward difference is proportional to (often written as /but we will not use this notation in the present bookwe can now plug in the forward difference in our differential equation sampled at the arbitrary mesh point tn unc un un tn / ( or with utd ru in our special model problem for population growthunc un run ( if depends on timewe insert tn for in this latter equation the fourth step is to derive computational algorithm looking at ( )we realize that if un should be knownwe can easily solve with respect to unc to get formula for at the next time level tnc unc un tf un tn ( provided we have known starting valueu we can use ( to advance the solution by first computing from then from from and so forth such an algorithm is called numerical scheme for the differential equation and often written compactly as unc un tf un tn / ( this scheme is known as the forward euler schemealso called euler' method in our special population growth modelwe have unc un run ( we may also write this model using the problem-specific symbol instead of the generic functionn nc rn nn ( the observant reader will realize that ( is nothing but the computational model ( arising directly in the model derivation the formula ( ariseshoweverfrom detour via differential equation and numerical method for the differential equation this looks rather unnecessarythe reason why we bother to