Exercise 5.3 [Fourth order R-K Method]

EXERCISE 5.3 [Fourth order R-K Method]

Evaluate using Fourth order R-K Method

1. Find y (0.2) given dy / dx = - xy, y(0) = 1, taking h = 0.2 by R-K method

of 4th order.

[Ans . 0.9802]

2. Find y (0.2) given y' = 3x + 1/2 y, y (0) = 1 by using Runge-Kutta method

[Ans. 1.15722]

3. Use Runge-Kutta method to approximate y, when x = 0.1, 0.2,02

0.3, h = 0.1 given x = 0 when y = 1 and dy/dx = x + y.

 [Ans. y (0.1)= 1.1103, y (0.2) = 1.2428, y (0.3) = 1.3997]

4. Using Runge-Kutta method of fourth order, find y (0.1) and y (0.2) correct to four places of decimals if (y + x) = dy/dx = y - x, y(0) = 1.

 [Ans. y (0.1)= 1.0911, y (0.2) = 1.1678]

5. Using Runge-Kutta method of fourth order find y (0.2), y (0.4) and y (0.6), correct to four places of decimals when

dy/dx = y - x², y (0) = 1.

 [Ans. y (0.2) = 1.2185, y (0.4)= 1.4682, y (0.6) = 1.738]

6. Using Runge-Kutta method of fourth order, find y for x = 0.1, x = 0.2, x = 0.3 given that dy/dx = xy + y², y (0) = 1.

 [Ans. y (0.1) 1.1168, y (0.2) = 1.2740, y (0.3)= 1.488] [A.U N/D 2014]

7. Using Runge-Kutta method of fourth order, find y (0.2), y (0.4) and y (0.6) given dy/dx  = y - x, y (0) = 2 taking h = 0.2.

[Ans. y (0.2) = 2.421, y (0.2) = 2.892, y (0.6) = 3.422]

8. Given dy/dx = x³ + y/2, y (1) = 2, find y (1.1) and y (1.2) using Runge-Kutta method of fourth order.

[Ans. y (1.1) = 2.2213, y (1.2) = 2.4914]

9. Solve the initial value problem dy / dx = 3x - 4y, y (0) = 2 at x = 0.4 taking h = 0.2 by Runge-Kutta method of fourth order.

[Ans. y (0.4) = 0.5543]

10. Find y (0.2) by Runge-Kutta method of fourth order if[A.U, May 1999]

 y'' - xy' = 0, y (0) = 1,y (0) = 0

11. Use fourth order Runge-Kutta method to compute y for x = 0.1given

y' = xy² - y², y (0) = 1, y' (0) = 0 [A.U, May 1999]

12. Apply fourth order Runge-Kutta method to find y (0.2) given

y = x + y, y(0) = 1  [A.U A/M 2019 R-13]