Numerical Methods — CACS252 (4th Sem)

__ fir Tribhuvan University | xO Faculty of Humanities & Social Sciences hi Le OFFICE OF THE DEAN ey 2023 Bachelor in Computer Applications Full Marks: 60 Course Title: Numerical Methods Pass Marks: 24 Code No: CACS252 Time: 3 hours Semester: IV Batch: 2020 Candidates are required to answer the questions in their own words as far as possible. Group B Attempt any SIX questions. [6x5 = 30] 2. Define error. Explain the Taxonomy Errors. [1+4] ‘3. Estimate the value of sin @ at 9 = 45° using Newton’s backward difference formula from the ~ — following set of data. [5] 60 [sin 6 | 0.1736 | 0.3420 | 0.5000 | 0.6428 | 0.7660 | 0.8660 | 4. Write an algorithm and program to calculate integration using Trapezoidal rule. ets] 5 What is the form of resultant matrix using Gauss-Jordan method? Solve the following system <* of equations using Gauss-Jordan Method. {1 + 4] x+2y-3z=4 : 2x + 4y -6z=8 - 2 x—2y+5z=4 6. Define ordinary differential equation. Use the fourth order Runge-Kutta method to estimate } y(0.4) of the equation = = x? + y? with y(0) = 0 assuming that h = 0.2. [1+ 4] 7. Solve for the steady-state temperatures in a rectangular plate of 8cm x 10cm, if one 10cm side is held at 50°C, and the other 10cm side is held at 30°C and other two sides are held at 10°C. ssume grids of size 2cm x 2cm. [5] Wit a short note on (Any Two): [2.5 +2.5] ~ a) Linear Interpretation b) Boundary value problems d) Partial Differential Equations Group C Attempt any TWO questions. [2x10 = 20] 9. Write an algorithm and program to compute the root of nonlinear equation using Newton - Raphson method. [4 + 6] 1Q. a) Fit a straight line to the following set of data using Least Square Regression. [5] 2 ry [3 [51617] 9| b) Apply the factorization method (any) to solve the equations: [5] SS 3x4 2y+7z=4 Ix+3y+z=5 8x+4y+z=7 hile 2 Write and implement an algorithm to solve the system of linear equations using Gauss-Seidel method with suitable numerical example. [256+ 2.5] b) Write a program to solve the ordinary differential equations using Heun’s method. [5]