University of PunePractical Examination April/May 2015SUBJECT: NUMERICAL METHODS AND OPTIMISATION Marks:50 Time: 2hr---------------------------------------------------------------------------------------------------------------------------

SET-AQ1. Write the program on Gauss-Elimination Method with Solver. Also draw the Flowchart for the same. Given: Solve 1) x+3y+3z=16; 2) x+4y+3z=18; 3) x+3y+4z=19. 30 MARKS ORQ1. Write the program on Lagranges interpolation with Solver. Also draw the Flowchart for the same. Given: Find y at x=1.5 for the following data.x0125

y2312147

30 MARKSQ2. Write the program on Newton-Raphson Method with Solver. Also draw the Flowchart for the same. Given: Find root of f(x)=0.51x-sin(x)=0; do 3 iterations. 20 MARKSORQ2. Write the program on successive approximation with solver, Also draw the Flowchart for the same. Given: f(x)= x2- 8x +6 =0 with accuracy criteria of 0.01 20 MARKS

SET-BQ1. Write the program on Gauss-Elimination Method with Solver. Also draw the Flowchart for the same. Given: Solve 1) x+3y+3z=16; 2) x+4y+3z=18; 3) x+3y+4z=19. 30 MARKSORQ1. Write the program on inverse interpolation Method with Solver. Also draw the Flowchart for the same. Given: Find x at y=2.5 for given data. x0123

y01725

30 MARKS

Q2. Write the program on Newton-Raphson Method with Solver. Also draw the Flowchart for the same. Given: Find root of f(x)=cos(x)-xex =0; accuracy=0.0001. 20 MARKSORQ2. Write the program on Rung- Kutta 4th order Method with Solver. Also draw the Flowchart for the same. Given: dy/dx= 1+y2 ; where y=0 when x=0. Find y(0.4) h=0.2. 20 MARKS

SET-CQ2. Write the program on Gauss-Elimination Method with Solver. Also draw the Flowchart for the same. Given: Solve 1) 3x+y-z = 1; 2) x+2y+z = 2; 3) x-y+4z = 3.30 MARKSORQ2. Solve dy/dx=x+2y using RK2. y(0)=0.1. Find y(0.2). Take h=0.1.

30 MARKS

Q1. Write the program on Simpsons 1/3rd rule with Solver. Also draw the Flowchart for the same. Given: Find integration of f(x)=ex-x3-2x+1; with limits 1 to 4. n=6 20 MARKSORQ1. Write the program on Gauss-Legendre 3point formula with Solver. Also draw the Flowchart for the same. Given: find integration of x2-8x+1 with limits 0 to 1. 20 MARKS

SET-D

Q2. Write the program on Gauss-Seidal Method with Solver. Also draw the Flowchart for the same. Given: Solve 1) 4x+y+2z=12; 2) x+3y+z=16; 3) x+2y+5z=10. 30 MARKSORQ2. Write the program on Inverse interpolation with Solver. Also draw the Flowchart for the same. Given: Find x at y=167for the following data.x1257

y112117317

30 MARKSQ1. Write the program on Gauss-Legendre 3point formula with Solver. Also draw the Flowchart for the same. Given: find integration of x2-3x+1 in limits 1 to 4. 20 MARKSORQ1. Write the program on Runge-Kutta 2th order method with Solver. Also draw the Flowchart for the same. Given: Solve dy/dx= x2+y2 y(0)=0 Estimate y(0.3), h=0.1 20 MARKS

SET-E

Q1. Write the program on Inverse interpolation interpolation with Solver. Also draw the Flowchart for the same. Given: Find x at y=450 for the following data.x571113

y15039214522366

30 MARKSORQ1. Solve dy/dx=x+y using RK2. y(0)=0.1. Find y(0.2). Take h=0.1.

30 MARKS Q2. Write the program on Simpsons 1/3rd rule with Solver. Also draw the Flowchart for the same. Given: Find integration of f(x)=x3-3x2+6x+8; with limits 0 to 1.5. n=320 MARKSORQ2. Write the program on Trapezoidal rule with Solver. Also draw the Flowchart for the same. Given: find integration of ex-sinx in limits 0 to 2. n=4 20 MARKS

SET-FQ1. Write the program on Gauss-Seidal Method with Solver. Also draw the Flowchart for the same.Given: Solve 1) 4x-3y-z = 11; 2) x+5y-2z = 12; 3) 2x-y+6z = 1430 MARKSORQ1. Write the program on Lagranges interpolation with Solver. Also draw the Flowchart for the same. Given: Find y at x=6 for the following data.x1257

y112117317

30 MARKS Q2. Write the program on Simpsons 1/3rd rule with Solver. Also draw the Flowchart for the same. Given: Find integration of f(x)=x3-3x2+6x+8; with limits 0 to 1.5. n=320 MARKSORQ2. Write the program on Simpsons 1/3rd rule with Solver. Also draw the Flowchart for the same. Given: Find integration of f(x)=x3-3x2+6x+8; with limits 0 to 1.5. n=3

20 MARKS

SET-GQ1. Write the program on Gauss-Elimination Method with Solver. Also draw the Flowchart for the same. Given: Solve 1) 10x+y+z=12; 2)2 x+10y+z=13; 3) 2x+2y+10z=14. 30 MARKSORQ1. Write the program on PDE Explicit Method with Solver. Also draw the Flowchart for the same. Given: Solve , for the following condition at x=0 and x=0.5, u=1 for all values of t at t=0, u=2x+1for0