In this video I go over an example on Euler's Method for numerically approximating solutions to a differential equation and this time look at the initial-value problem: y' = x + y with y(0) = 1. Initially I use the step size of 0.1 to roughly approximate the solution at x = 0.1, 0.2, ..., 1.0. But to get more accurate approximations we can decrease the step size even further. As shown in this video, when we decrease the step size further and further the solution approaches closer and closer to the exact value. This is a very useful video to understand Euler's method in detail, as well as how to develop spreadsheets to calculate it, so make sure to watch this video!
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Excel Notes: https://1drv.ms/x/s!As32ynv0LoaIhsQnSuqAQ7rhC3PsFg
View Video Notes on Steemit: https://steemit.com/mathematics/@mes/differential-equations-euler-s-method-example-1
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I don't always approximate differential equations using Euler's Method but when I do I usually decrease the step size until the solution approaches the exact solution ;)
View Video Notes on Steemit: https://steemit.com/mathematics/@mes/differential-equations-euler-s-method-example-1