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Course: MPZ 4230-Engineering Mathematics II Assignment No.02 Academic Year – 2012/2013 Instructions • Answer all questions • Write your address back of your answer scripts • Use both sides of paper when you are doing assignment. • Please send the answer scripts of your assignment on or before the due date to the

following address. Course Coordinator – MPZ 4230 Dept. of Mathematics & Philosophy of Engineering Faculty of Engineering Technology The Open University of Sri Lanka. Nawala, Nugegoda.

You can collect model answers from virtual class (www.ou.ac.lk)

1. Solve by Taylor’s series method of third order, the problem ( )3 2 xy x xy e−′ = + ,

( )0 1y = to find y for 0 1 0 2 0 3x . , . , .=

2. Given 1 0dx

tydt

− − = and 0dy

txdt

+ = , 0t = , 0x = , 1y = , evaluate ( )0 1x . , ( )0 1y . ,

( )0 2x . and ( )0 2y .

3. Using Taylor’s series method, obtain the value of y at 0 1 0 2 0 3x . , . , .= to four

significant figures if y satisfied the equation2

2 0d y

xydx

+ = , given that 12

dydx

= and 1y =

when 0x = .

4. Given that 32 2y x y′ = + , ( )1 2y = . Find y at 1 1 1 2x . , .= by using Runge – Kutta

method

a) Second order

b) Fourth order

Department of Mathematics & Philosophy of Engineering

Faculty of Engineering Technology

The Open University of Sri Lanka

Nawala - Nugegoda

5. Solve 2 2

2 22 2 8u u

x yx y

∂ ∂+ =∂ ∂

for square mesh given 0u = on the four boundaries dividing

the square into 9 sub squares of length one unit.

6. Obtain the numerical solution to solve2

25u ut x

∂ ∂=∂ ∂

, under the conditions ( )0 0u ,t = ,

( )8 100u ,t = and

( )0u x, =20 for 0 5100 for 5 8

x x

x

< ≤�� < ≤�

For five time step having 1h =

7. Solve the hyperbolic partial differential equation (vibration of springs) for one half of

period of oscillation taking h=1.

25tt xxu u= , ( ) ( )0 5 0u ,t u ,t= = , ( )0 0tu x, =

( )0u x, =2 for 0 2 510 2 for 2.5 5

x x .

x x

≤ <�� − ≤ ≤�