Question

explain Euler method.

Answer 1

the euler method is the first order numerical procedure for solving ordinary differential equation with given initial value.

Answer 2

Summary of Euler's Method

In order to use Euler's Method to generate a numerical solution to an initial value problem of the form:

y′ = f(x, y)

y(xo) = yo
decide upon what interval, starting at the initial condition, u desire to find the solution.then chop this interval into small subdivisions of length h. Then, using the initial condition as your starting point, generate the rest of the solution by using the iterative formulas:

xn+1 = xn + h

yn+1 = yn + h f(xn, yn)

to find the coordinates of the points in your numerical solution. terminate this process when uhave reached the right end of the desired interval.

An Example


y′ = x + 2y

y(0) = 0

numerically, finding a value for the solution at x = 1, and using steps of size h = 0.25.