Question

Compare Euler and extended Euler for solution of x' = 1 + x2 + t3 for x(t=2) given x(t=1) = -4 using 10 points. Report the percent difference of from “exact" value x(t=2) = 4.371221866 for the 2 methods

Matlab script? Command Window? And Solve?

Answer 1

x1=0.0

x=0

t=0

%%For T=1 we find the value of x'

x=-4

t=1

x1=1+(x*x)+(t*t*t)

Now this is the general algorithm to solve the ruler method put the values and you will get the ans

%% the Initial conditions and setup

h = (enter your step size); % step size

x = (enter the starting value of x ):h:(enter the ending value of x); % the range of the x value entered

y = zeros(size(x)); % allocate the result of the subject y

y(1) = (enter the starting value of y ); % the initial y value is inserted

n = numel(y); % the number of y values present

% The loop to solve equation

for i=1:n-1

    f = the expression for x'

    y(i+1) = y(i) + h * f;

end