Statistics and Numerical Methods: Unit V: Numerical Solution of Ordinary Differential Equations
Exercise 5.3 [Fourth order R-K Method]
Solved Example Problems
Evaluate using 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]
Statistics and Numerical Methods: Unit V: Numerical Solution of Ordinary Differential Equations : Tag: : Solved Example Problems - Exercise 5.3 [Fourth order R-K Method]
Statistics and Numerical Methods: Unit V: Numerical Solution of Ordinary Differential Equations
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Statistics and Numerical Methods
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