Consider the following initial value problem: y = 5xy; y(0) = 2 Use the Runge-Ku

Question

Consider the following initial value problem: y = 5xy; y(0) = 2 Use the Runge-Kutta method to find approximate values for y at each of the points x = 0.1, 0.2, 0.3, and 0.4. Use a step size of h = 0.1. Fill in the values you obtain in the following table (do all of your calculations to exactly eight decimals, but at each step round the value you place in the table for y to exactly four decimal places):

Explanation / Answer

y0 =y(0)=2 ; y1=y(0.1); y2=y(0.2); y3=y(0.3); y4=y(0.4); f(x,y) =5xy h=0.1 =>y1= y0+h f(x,y) y1= 2+ 0.1(5 *0 *2) y1=2 =>y2= y1+h f(x,y) y2= 2+ 0.1(5 *0.1 *2) y2=2.1 =>y3= y2+h f(x,y) y3= 2.1+ 0.1(5 *0.2 *2.1) y3=2.31 =>y4= y3+h f(x,y) y4= 2.31+ 0.1(5 *0.3 *2.31) y4=2.6565

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