Chapter 8 Section 85 Question o6c Determine approximate valu

Chapter 8, Section 8.5, Question o6c Determine approximate values of the solution x- 4 (t), y- (t) of the given initial value problem at t 0.2, 0.4, 0.6, 0.8, and 1.0 use the Runge-Kutta method with h 0.1 sin(x 4 y), x(0) 1, y( 0 COS X, Use a computer or graphing calculator to solve this problem. Round your an swers to five decimal places. n 6 n m 4 n 10 02 0.4 06 08 1.0

Solution

Solution for Question 1

code

1) First create a function and save it as f1.m

contents of f1:

function dydt = f1(t,y)

dydt = [exp(-y(1)+ y(2))- cos(y(1)); sin(y(1)-4*y(1))];
end

2) Set Options for ode45 solver

opts_1 = odeset(\'InitialStep\',0.1,\'MaxStep\',0.1);

3)Solve DE as

[t,y]=ode45(@f1,[0 5],[1;3],opts_1);

y gives vector whose first column are value of X and second column are value of Y. To find value at point any instant t0:

sol= y((t==t0),:)

t	0.2	0.4	0.6	0.8	1
x	1.9845	2.5331	2.9824	3.3323	3.6393
y	3.1409	3.0527	2.8871	2.8987	3.0653