ACME Engineering College, Sitapaila, Kathmandu

Note: Tutorial Should be submitted within 7 days of announcement in class. Prepared by: Krishna Gaihre

Numerical Method Tutorial-2 Civil B-III/I

Chapter - 5

1. Solve following Linear Algebraic Equation

a. Use Gauss elimination method to solve the equation

4X1+5X2-6X3=28

2X1-7X3=29

-5X1-8X2=-64 Use partial pivoting method.

b. Use Gauss Jordan Method to solve the above equation.

2. Use gauss Jordan method

10X1-3X2+6X3=24.5

X1+8X2-2X3=-9

-2X1+4X2-9X3=-50

3. Solve the following equation

i. 4X1-2X2-X3=39

X1-6X2+2X3=-28

X1-3X2+12X3=-86

a. By Gauss elimination method b. Gauss Jordan Method

ii. X1+X2=X3=2

2X1+3X2+5X3=-3

3X1+2X2-3X3=6

a. Use elimination with partial pivoting method

4. Solve following equation. A] Use Dolittle Method B] Crout Method

X1+X2-X3=2

2X1+3X2+5X3=-3

3X1+2X2-3X3=6

5. Find Largest Eigen Value and Corresponding Eigen Vector of Given matrix using power method.

1 2 0

2 1 0

0 0 -1

6. Solve Q. No. 3-i equation by following Iterative Method.

a. Jacobi method b. Gauss Seidal Method

Chapter - 4

7. Evaluate ∫ (𝑥² + 2𝑥 + 1)/(1 + ((𝑥 + 1)2)² )2

0 dx, by using Gaussian Integration of 2 point and 3

point formula.

8. Evaluate the integral ∫ (𝑥

𝑠𝑖𝑛𝑥)

1

.5dx using Romberg Method

Chapter - 6

9. Solve the following equation for y(0.2) 𝑑²𝑦

𝑑𝑥²+ 2

𝑑𝑦

𝑑𝑥− 3𝑦 = 6𝑥 , given that y(0)=0, y’(0)=1, Use RK-4 Method.

𝐂𝐡𝐚𝐩𝐭𝐞𝐫 − 𝟕

10. Solve the Poisson’s equation uxx +uyy=-81xy, 0<x<1, 0<y<1 given that u(0,y)=0, u(x,0)=0 &

u (1,y)=100 & u (x,1)=100 & h=1/3.