Euler's method for a first order IVP y' = f(x, y), y(xo) = yo is the the following algorithm. From (co, yo) we define a

[answerhappygod]

Euler S Method For A First Order Ivp Y F X Y Y Xo Yo Is The The Following Algorithm From Co Yo We Define A 1 (126.03 KiB) Viewed 42 times

Euler's method for a first order IVP y' = f(x, y), y(xo) = yo is the the following algorithm. From (co, yo) we define a sequence of approximations to the solution of the differential equation so that at the nth stage, we have In xn-1+h, Yn = Yn-1 + h⋅ f(xn-1, Yn-1). In this exercise we consider the IVP y' = -x + y with y(1) = -1. This equation is first order linear with exact solution y = 1 + x - 3e-1. Use Euler's method with h = 0.2 to approximate the solution of the differential equation. For this example we include the slope field to give a rough idea what the shape of the solution should look like. We have also plotted the exact solution y = 1 + x - 3eª-1 over a small interval. Apply Euler's method to complete the following table: In the first two rows enter the values of an and yn and in the third row use the exact solution to find the errors en = |y(xn) - Yn. A calculator or other scientific software would be handy to work these types of problem. You can always use answers given by explicit formulas which are very accurate. You need at least 4 significant digits. If your answer is marked wrong try entering a more accurate answer. n = 0 xn 1 Yn -1 en 0 1 2 3 4