Question
Suppose that we use Euler's method to approximate the solution to the differential equation
šš¦/šš„=š„^4/š¦ š¦(0.1)=1
Let š(š„,š¦)=š„^4/š¦.
We let š„0=0.1 and š¦0=1 and pick a step size ā=0.2. Euler's method is the the following algorithm. From š„š and š¦š, our approximations to the solution of the differential equation at the nth stage, we find the next stage by computing
šš¦/šš„=š„^4/š¦ š¦(0.1)=1
Let š(š„,š¦)=š„^4/š¦.
We let š„0=0.1 and š¦0=1 and pick a step size ā=0.2. Euler's method is the the following algorithm. From š„š and š¦š, our approximations to the solution of the differential equation at the nth stage, we find the next stage by computing
Answers
Damon
at (0.1 , 1 )
slope = dy/dx = (0.1)^4 /1 = (10^-1)^4 = 10^-4
at x = x + h = 0.1 + 0.2 = 0.3
Using Euler
our guess at y = 1 + h (dy/dx) = 1 + 0.2 * 10^-4 = 1 +0.00002 = 1.00002
slope = dy/dx = (0.1)^4 /1 = (10^-1)^4 = 10^-4
at x = x + h = 0.1 + 0.2 = 0.3
Using Euler
our guess at y = 1 + h (dy/dx) = 1 + 0.2 * 10^-4 = 1 +0.00002 = 1.00002