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  3. y'=y-x^2 ; y(1)= -4 my matlab program won't work.

y'=y-x^2 ; y(1)= -4 My MATLAB program won't work. I am trying to get the main program to...

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Verified Solution

Question

Mechanical Engineering

y'=y-x^2 ; y(1)=-4

My MATLAB programwon't work. I am trying to get the main program to output a plot ofthe three equations (1 from the main program and two called in thefunction). The goal is to code a Euler method and a 2nd orderTaylor numerical solution for

a. x0= 1.0 , step sizeh= 0.2, # of steps n=20

b. x0= 1.0 , step sizeh=0.05 , # of steps n=80 ; write a separate functionn for f(x,y)that is called. Plot the results on the same plot as the exactsolution.

I keep getting anerror of \"Matrix Dimensions must agree ; error in Project_2(myfunction) with my Tay = ... equation (2nd order taylorequation).

Main Code

t_span = 1:0.2:5;
h=0.2;
y1 = -4;
B=(t_span.^2);
[x,y] = ode45(@(x,y) y-x^2, t_span, y1);
d=[x,y];
project_2(y1,h,d,B)

subplot(4,1,1)
plot(x,y)

xlabel('value of x')
ylabel('value of y(x)')
grid on

t_span = [1:0.05:5];
y1 = -4;
h=0.05;
[x,y]= ode45(@(x,y) y-x^2, t_span, y1);
subplot(4,1,4)
project_2(y1,h,d,B)
plot(x,y)
xlabel('value of x')
ylabel('value of y(x)')
grid on

The Function

function[outputArg,Tay] = project_2(y1,h,d,B)

outputArg = y1 + h*d; %Euler method

Tay= y1+(h*d)+((1/2)*(h^2))*((y1-2*t_span)+(-B)*d); %2nd order Taylor

subplot(4,1,2)
plot(outputArg)

subplot(4,1,3)
plot(Tay)

end

Answer & Explanation Solved by verified expert
4.3 Ratings (561 Votes)
tspan 1025h02y1 4Btspan2xy ode45xy yx2 tspan y1dxyoutputArgTay project2y1hdBtspansubplot321plotxyxlabelvalue of    See Answer
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