SRM University 2007 B.Tech Food Process Engineering NUMERICAL SOLUTIONS OF ORDINARY DIFFERENTIAL EQUATIONS - Question Paper

NUMERICAL SOLUTIONS OF ORDINARY DIFFERENTIAL EQUATIONS
MA 252
UNIT – IV

PART – A
1. Define step – by – step method (or) marching method
2. Give 2 examples for step – by step method
3. Define initial value issue
4. Define final value issue
5. Write the taylor’s series expansion for finding the numerical solution of the formula with y (xo) = yo
6. Write any 2 multi – step method
7. Write the merits and demerits of the Taylor’s series methods.
8. Write the Euler’s methods formula for finding the solution of a firsr order differential formula
9. What is the formula for replaced Euler’s method of finding the solution a 1st order differential formula
10. Write the Runge – Kutta 2nd order formula for finding the solution of a 1st order differential formula
11. Write the Runge – Kutta IV order formula for solving O.D.E
12. Write the formula for Milne’s predicator corrector firmula.
13. Write the formula for Adams – Bashforth predictor – corrector formula.
14. Milne’s and adam’s methods are requires info about past _______ points, to predict the ________ value.
15. Write the Distinguishing properties of Runge – Kutta method
16. R.K method of 2nd order in also called _________ method
17. Write the difference ranging from Euler’s method and replaced Euler’s methods
18. Write any 2 multi – step methods.
19. By taylor series, obtain y (1.1) provided y1 = x+y, y (1) = 0
20. Using Euler’s method obtain y (0.2) provided y1 = x + y, y (0) = 1.

PART – B
1. Use Euler’s method to approximate y when x = 0.1, provided that with y = one
for x = 0
2. Solve the formula = one – y with the initial condition x = 0 , using Euler’s algorithm and tabulate the solutions at x = 0.1, 0.2. 0.3
3. Given that = log (x+y) with the initial condition that y = one when x = 0 , use Euler’s replaced method to obtain y for x = 0.2, and x = 0.5 in more circulate form.
4. Solve numerically, using Taylor series approach = x+y, starting with x0 = 1, y0 = 0
and carrying up x = 1.2, taking h = 0.1 compare the final outcome with the value of the explicit solution.
5. Use Taylor’s series method to obtain y for x = 0.1 accurate to 4 places & provide that with y0 = 1, xo = 0
6. Using Taylor series method, find the values of y at x = 0.1 (0.2) (0.3) to 4 significant figures, if y satisfies the formula provided that =0.5 and y = one when x = 0
7. Solve the subsequent initial value issue involving 2 independent function x (t) and
y (t) using Taylor’s series method Evaluate x and y at
t = 0.1, 0.2.
8. Use Runge – kutta method to solve y one = xy for x = 1.4 Initially x = 1, x = two
( taken h = 0.20)
9. Solve for x = 0.5 to x =2 by using R –K 2nd order method with x0¬ = 0, yo = one (take h = 0.5)
10. Using Runge – Kutta method, solve for x = 0.1, initially y (0) = 2, take h = 0.1
11. Solve the initial value issue y1 = x + y, y (0) = 0, by runge – kutta method, choosing the interval to be 0.2.
12. Solve the R – K method provided that xo = 1, y = -1, to = 0
13. Use Milne’s method to solve numerically the formula with initial condition
xo = 0, yo = 1
14. Solve the initial value issue for x = 0.4 by using Milne’s method, when it is provided that
X : .1 . 2 . 3
Y : 1.105 1.223 1.355
15. Solve the differential formula y1 = x2 + y2 – 2, using Milne’s predictor method for x = 0.3, provided the initial value x =0, y = 1. The values of y for x = - 0.1, 0.1 and 0.2. should be calculated by a Taylor’s series expansion.
16. Given and y (0) = 1, y (0.1) = 1.06, y (0.2) = 1.12, y (0.3) = 1.21 evaluate y (0.4) by Milne’s predictor – corrector method.
17. Given y1 = x2 – y; y (0) = one and the starting values y (0.1) = .90516, y (0.2) = .82127,
y (0.3) = .74918 find the values of y (o.4) and y (0.5) using Adams – Bashtooth P. C
method.
18. Using Adams – Bash forth formula, determine y (0.4) provided the differential formula xy and the data.
X : 0 0.1 0.2 -0.3
Y : 1 1.0025 1.0101 1.0228

Earning:   Approval pending.