Use Improved Eulers Method with a step size of h = 0.1 to approximate the soluti
ID: 1949564 • Letter: U
Question
Use Improved Eulers Method with a step size of h = 0.1 to approximate the solution to the initial value problem dy/dx =x?y , y(1)=4 at x=1.4
Explanation / Answer
Use Eulers Method with a step size of h = 0.1 to approximate the solution to the initial value problem dy/dx= x sqrt(y), y(1)=4 ==> x0 =1 AND y0 =4 OR y(x0 )=4 at x=1.4 FIND y(1.4) = ? y' = f(x,y) = x sqrt(y) y(xn+h) = y(xn) + h (xn sqrt(y(xn ) ) Euler's Method y(xn+0.1) = y(xn) + 0.1 (xn sqrt(y(xn ) ) if n=0 and x0 =1 and y0 =4 y1 =y(x0+0.1) = y(x0) + 0.1 (x0 sqrt(y(x0 ) ) y1 =y(1+0.1) = 4 + 0.1 ( 1 sqrt(4) ) = 4.2000 ==> y(1.1) =4.2000 if n=1 and x1 =1.1 and y1 =4.2 y2 =y(x0+0.2) = y(x1) + 0.1 (x1 sqrt(y(x1 ) ) y2 =y(1+0.2) = 4.2 + 0.1 ( (1.1) sqrt(4.2) ) = 4.4254 ==> y(1.2) = 4.4254 if n=2 and x2 =1.2 and y2 =4.4254 y3 =y(x0+0.3) = y(x2) + 0.1 (x2 sqrt(y(x2 ) ) y3 =y(1+0.3) = 4.4254 + 0.1 ( (1.2) sqrt(4.4254) ) = 4.6778 ==> y(1.3) = 4.6778 if n=3 and x3 =1.3 and y3 = 4.6778 y4 =y(x0+0.4) = y(x3) + 0.1 (x3 sqrt(y(x3 ) ) y4 =y(1+0.4) = 4.6778 + 0.1 ( (1.3) sqrt(4.6778) ) = 4.9590 ==> y(1.4) = 4.9590
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