Question

Please help:)
Solve the initial value problem \(dy/dx=\frac{1}{2](x+y)-1\), \(0\le x\le0.3\), \(y(0)=1\), using fourth-order Runge-Kutta method with h=0.1. Compare your results with the analytical solution \(y=e^{\frac{x}{2}}-x\) to this differential equation.

Answer 1

this sounds like you need a computer program. what language?

Answer 2

No. I am learning this under maths, numerical analysis.

Answer 3

I am k with the first part of the question bt am stuck in the comparision part.

Answer 4

You have to evaluate a number of expressions at every step. It looks like they want 3 steps 0 to 0.3 in steps of 0.1
so you could do it with a calculator

Answer 5

ya. bt hw abt the comparision part.

Answer 6

\(y=e^{\frac{x}{2}}-x\)
plug in x=0.3 and evaluate. compare to your answer using runge-kutta

Answer 7

bt y specifically 0.3

Answer 8

x= 0.3 y will be 0.862

Answer 9

ok so I shoud check if I get the same when I solve dy/dx=1/2(x+3)-1 using range-kutta method for x=0.3

Answer 10

@phi

Answer 11

Here is a bit of matlab

y=1; h=0.1; x=0;
for ii=1:3
k1= h*fff(x,y);
k2= h*fff(x+h/2,y+k1/2);
k3= h*fff( x+h/2, y+ k2/2);
k4= h*fff( x+h,y+k3);
y= y+ (k1+2*k2+2*k3+k4)/6
x= x+h
end

where fff(x,y) is defined as
function z=fff(x,y)
z= 0.5*(x+y)-1;

I still have to check if I did this correctly...

Answer 12

ha k

Answer 13

The matlab gives
y= 0.861834234021667

the exact answer e^(0.15)-0.3 = 0.861834242728283

Answer 14

Here are the partial results

Step 1: x0= 0.000000 y0= 1.000000
k1 = -0.050000000000000
k2 = -0.048750000000000
k3 = -0.048718750000000
k4 = -0.047435937500000
y = 0.951271093750000

Step 2: x1= 0.100000 y1= 0.951271
k1 = -0.047436445312500
k2 = -0.046122356445313
k3 = -0.046089504223633
k4 = -0.044740920523682
y = 0.905170912554321

Step 3: x2= 0.200000 y2= 0.905171
k1 = -0.044741454372284
k2 = -0.043359990731591
k3 = -0.043325454140574
k4 = -0.041907727079313
y = 0.861834234021667


y =0.861834234021667
x =0.300000000000000

Answer 15

any luck?

Answer 16

trying

Answer 17

wat's the problem here? i mean with the second part?
i think it's straight forward.....did i miss smthin?