Question

Using the Script:

function EulerMethod1(n)

X = 0 : 1/n : 1 ;

Y = zeros( 1, n + 1 ) ;

Y(1) = 1 ;

for k = 1 : n

m = Y(k) ;

Y(k + 1) = Y(k) + m*( X(k + 1) - X(k) ) ;

end

clf

plot( X, Y )

Create a new script, which defines the function EulerMethod2. The purpose of EulerMethod2 is to use Euler's Method to approximate the solution to the Initial Value Problem given below.

      dy/dx = 2xy        where.           y (0) = 1.          over the interval. [ 0, 2 ]

Answer 1

Required Matlab code with explanatory comments where changes were made is given below:

function EulerMethod2(n)

X = 0 : 1/n : 2 ; %changed to 0:1/n:2 as we need solution over [0 2]

Y = zeros( size(X) ) ; %change so Y and X have same sign

Y(1) = 1 ;

for k = 1 : length(X)-1

m = 2*X(k)*Y(k) ; %changed to y'=f(x,y)=x*y

Y(k + 1) = Y(k) + m*( X(k + 1) - X(k) ) ;

end

clf

plot( X, Y )

Resulting plot:

Hope this was helpful. Please do leave a positive rating if you liked this answer. Thanks and have a good day!