Malviya National Institute of Technology, Jaipur Department of Mathematics ME-206 (Engineering Mathematics-III) Tutorial Sheet #5 1.

1. Given dy/dx=xy1/3, y(1)=1. Find y when x=1.1 and h=0.1 using (a) Euler’s formula (b) Euler’s modified formula (c) Runga Kutta 4 th order methods. 2.

Given dy/dx=1+y2, y(0)=0 Find y(0.6) taking h=0.2.

3.

Given dy/dx=(x+y)-1, x0=0, y0=1. Find y when x=1.5 and h=0.5 using (1) Runga Kutta 4th order method (2) Euler’s modified method.

dy = x + y 2 . Use Runge-Kutta method to find an approximate value of y for x=0.2 given that dx y=1 when x=0 for h=0.1.

4.

5.

If

Given

dy = x2 + y , y(0)=1. Determine (i)y(0.02) (ii) y(0.04) (iii) y(0.06) using Euler’s modified dx

method. dy 6. Use the Runge-Kutta Method of IV order to solve 10 = x2 + y 2 , y(0)=1 for the interval 0
7. Using Euler’s modified formula, find an approximate value of y when x=0.3, given that dy/dx=x+y and y=1 when x=0. 8. Using Euler’s modified formula, solve dy/dx=1-2xy given y=0 at x=0 from x=0 to x=0.6 taking the interval h=0.2. 9. Write the modified Euler method for solving the first order initial value problems in the Runge-Kutta formulation. 2

10.Employ Runge-Kutta method to find y for x=0.2 from

d2y  dy  = x  − y 2 given that y=1, dy/dx=0 2 dx  dx 

for x=0. 11.For the following figure evaluate u(x,y) satisfying Laplace,s equation point of the figure: 100

100

100

100

200

u1

u2

50

200

u3

u4

0

100

50

0

0

∂2u ∂2 u + 2 = 0 at the pivotal ∂x 2 ∂y

## Malviya National Institute of Technology, Jaipur Department of ...

Malviya National Institute of Technology, Jaipur. Department of Mathematics. ME-206 (Engineering Mathematics-III). Tutorial Sheet #5. 1. 1. Given dy/dx=xy1/3, ...

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