Engineering Board Exam Reviewer · Numerical Methods · hard
Use one step of the fourth-order Runge-Kutta method with h=0.2 to estimate y(0.2) for y'=x+y, y(0)=1.
- 1.2
- 1.24
- 1.2428
- 1.2432
Answer
C. 1.2428
Solution
k1=f(0,1)=1. k2=f(0.1,,1+0.1k1)=f(0.1,1.1)=1.2. k3=f(0.1,,1+0.1k2)=f(0.1,1.12)=1.22. k4=f(0.2,,1+0.2k3)=f(0.2,1.244)=1.444. Then y1=1+0.2/6(1+2(1.2)+2(1.22)+1.444)=1+0.2/6(7.284)=1.2428.
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