Approximate y(1,2), with h = 0.1 given that x y' = y -2x^2, y(1)=2, by RK-4 using 5-digits rounding.

Emeli Hagan 2021-02-18 Answered
Approximate y(1,2), with h = 0.1 given that xy=y2x2,y(1)=2, by RK-4 using 5-digits rounding.
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dieseisB
Answered 2021-02-19 Author has 85 answers

Step 1
To approximate y(1.2)by RK-4
Given h=0.1 and xy=y2x2,y(1)=2
y=yx2x
Here f(x,y)=yx2x
Fourth order RK method is given by
k1=hf(x0,y0)
=(0.1)f(1,2)
=(0.1)(0)=0
k2=hf(x0+h2,y0+k12)
=(0.1)f(1.05,2)
=(0.1)(0.19524)
=0.01952
k3=hf(x0+h2,y0+k22)
=(0.1)f(1.05,1.99024)
=(0.1)(0.20454)
=0.02045
k4=hf(x0+h,y0+k3)
=(0.1)f(1.1,1.97955)
=(0.1)(0.40041)
=0.04004
y1=y0+16(k1+2k2+2k3+k4)
y1=2+16(0+2(0.01952)+2(0.02045)+(0.004004))
y1=1.986
Hence y(1.1)=1.98601
Step 2
Again taking (x1,y1)placeof(x0,y0) repeat the process
k1=hf(x1,y1)
=(0.1)f(1.1,1.98601)
=(0.1)

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