Short Questions and Answers

SHORT QUESTIONS AND ANSWERS

1. Write down the Runge-Kutta formula of fourth order to solve

dy / dx = f(x, y) with y (x₀) =y_u  [M.U, April 96, A.UCBT M/J 2010]

(or) Define fourth order R-K method.

 [A.U N/D 2012] [A.U A/M 2019 R-13]

Solution Refer See Page No. 5.33

2. State the special advantage of Runge-Kutta method over Taylor's series method. (OR) What are the distinguished properties of R-K Methods? [M.U, Oct. 96]

Solution :

Runge-Kutta method does not require prior calculation of higher derivatives of y (x), as the Taylor's method does. Since the differential equations using in applications are often complicated, the calculation of derivatives may be difficult.

3. Say True or False.

Modified Euler's method is the Runge-Kutta method of second order.

Solution: The statement is true.

4. State which is better. Taylor's method or R-K method? Why? (or) What are the advantages of R-K method over Taylor's method.

(or) [M.U. April, 1996, A.U CBT A/M 2011, A.U M/J 2014]

State the special advantage of R-K method over Taylor's method. [M.U. Oct. 1996]

(or)

Why is Runge-Kutta method preferred to Taylor's series method.  [M.U. April, 1998, CBT A/M 2011]

(or)

Compare Taylor's series and R-K Method. [M.U. April, 1997]

Solution:

R-K methods does not require prior calculation of higher derivatives of y (x) as the Taylor's method does.

Since, the differential equations using in applications often complicated, the calculation of derivatives may be difficult.

Also the R-K formulae involve the computation of f (x, y) at various positions, instead of derivatives and this function occurs in the given equation.

5. The fourth order Runge-Kutta methods are used widely in................... to differential equations. [M.U. Oct. 1998]

Solution: Getting numerical solutions.

6. Find the values of of k₁ and l₁ to solve y'' + xy' + y = 0, y (0) = 1, y' (0) = 0 by Fourth order R-K method?  [A.U Trichy A/M 2010] [A.U N/D 2011]

Solution :