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ENSH 251Bachelor in Geomatics Engineering · Semester 44 Papers Available

Numerical Methods

Past examination question papers and complete curriculum syllabus for Numerical Methods (ENSH 251), Bachelor in Geomatics Engineering Semester 4 under Institute of Engineering (IOE), Tribhuvan University.

Sem 4 Subjects (5)View Full Semester Overview →
ENSH 251Numerical MethodsENGE 251Engineering Survey IIENGE 252PhotogrammetryENGE 253Geographic Information System(GIS)ENSH 252Communication English
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Past Question Papers (PDF)

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4th-sem_Numerical Methods.pdf

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Most Frequently Asked Questions

Top recurring IOE board exam questions for Numerical Methods with verified mark schemes, formula notation, and recurrence frequency.

Showing 40 of 40 top repeated questions
6 Chapters · Click any chapter to expand
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Year-wise & Session-wise Exam Papers

Complete questions from each exam session (Regular & Back exams from 2082 to 2069) for Numerical Methods. Click any session paper to expand.

Showing 147 questions across 21 exam session papers
Institute of Engineering • 2083 Baishakh Board Examination
Q1[8 Marks]Solution of Non-Linear Equations
Find a real root of equation using secant method correct to fourth place of decimal.
Q2[8 Marks]Numerical Differentiation and Integration
Derive the formula for the first and second order derivative using Newton's forward interpolation formula. Also find the expressions at the initial point.
Q3[8 Marks]Solution of Partial Differential Equations
Solve the equation on the mesh bounded by and . The boundary values are
Q4[8 Marks]Solution of Ordinary Differential Equations (ODE)
Write a program code in python to solve initial value problem involving a first order initial value problem using Runge-Kutta second order method.
Q5[8 Marks]Solution of Partial Differential Equations
Solve the one-dimensional heat equation for two-time steps with using Crank-Nicolson method given that with initial and boundary conditions:

Curriculum Syllabus & Course Topics

Sourced from TU curriculum portal
Full Syllabus (PDF)
Chapter-wise Units & Micro-Syllabus Topics (6 Units)

  1. 1. Solution of Non-Linear Equations

    • 1.1Errors and accuracy in numerical computations
    • 1.2Bisection method
    • 1.3Regula Falsi method and secant method
    • 1.4Newton Raphson method
    • 1.5Fixed point iteration method
    • 1.6Comparison of the methods (Bracketing vs open-ended methods and rates of convergence)
    • 1.7Solution of system of non-linear equations
    • 1.7.1Direct approach
    • 1.7.2Newton Raphson method

  2. 2. Solution of System of Linear Algebraic Equations

    • 2.1Direct methods
    • 2.1.1Gauss Jordan method
    • 2.1.2Gauss elimination method, pivoting strategies (Partial and complete)
    • 2.1.3Matrix inverse using Gauss Jordan and Gauss elimination methods
    • 2.1.4Factorization methods (Do-Little’s method and Crout’s method)
    • 2.2Iterative methods
    • 2.2.1Jacobi’s method
    • 2.2.2Gauss-Seidal method
    • 2.3Determination of largest and smallest Eigen values and corresponding vectors using the power method

  3. 3. Interpolation

    • 3.1Polynomial Interpolation
    • 3.1.1Finite differences (Forward, backward, central and divided differences)
    • 3.1.2Interpolation with equally spaced intervals: Newton’s forward and backward difference interpolation, Stirling’s and Bessel’s central difference interpolation
    • 3.1.3Interpolation with unequally spaced intervals: Newton’s divided difference interpolation, Lagrange interpolation
    • 3.2Least square method of curve fitting
    • 3.2.1Linear form and forms reducible to linear form
    • 3.2.2Quadratic form and forms reducible to quadratic form
    • 3.2.3Higher degree polynomials
    • 3.3Cubic spline interpolation
    • 3.3.1Equally spaced interval
    • 3.3.2Unequally spaced interval

  4. 4. Numerical Differentiation and Integration

    • 4.1Numerical differentiation
    • 4.1.1Differentiation using polynomial interpolation formulae for equally spaced intervals
    • 4.1.2Local maxima and minima from equally spaced data
    • 4.2Numerical integration
    • 4.2.1Newton Cote’s general quadrature formula
    • 4.2.2Trapezoidal rule, Simpson’s 1/3 and 3/8 rules, Boole’s rule, Weddle’s rule
    • 4.2.3Romberg integration
    • 4.2.4Gauss-Legendre integration (up to 3-point formula)

  5. 5. Solution of Ordinary Differential Equations (ODE)

    • 5.1Initial value problems
    • 5.1.1Solution of first order equations: Taylor’s series method, Euler’s method, Runge-Kutta methods (Second and fourth order)
    • 5.1.2Solution of system of first order ODEs via Runge-Kutta methods
    • 5.1.3Solution of second order ODEs via Runge-Kutta methods
    • 5.2Two-point boundary value problems
    • 5.2.1Shooting method
    • 5.2.2Finite difference method

  6. 6. Solution of Partial Differential Equations

    • 6.1Introduction and classification
    • 6.2Finite difference approximations of partial derivatives
    • 6.3Solution of elliptic equations
    • 6.3.1Laplace equation
    • 6.3.2Poisson’s equation
    • 6.4Solution of parabolic and hyperbolic equations
    • 6.4.1One-dimensional heat equation: Bendre-Schmidt method, Crank-Nicolson method
    • 6.4.2Solution of wave equation

Examination Scheme & Marks Distribution

Evaluation Structure

  • Final Board Theory Exam: 60 Marks (Pass mark: 24)
  • Internal Assessment: 40 Marks (Pass mark: 16)
  • Practical / Lab Exam: 25 or 50 Marks (Continuous lab evaluation + viva, where applicable)

* This is the general current IOE 60/40 scheme; verify course-specific details in the syllabus above.

Exam Preparation Guidelines

  • Review the 4 available past examination papers to identify recurring patterns, core problem types, and chapter weightage.
  • Practice numerical problems step-by-step with clean formula derivations, clear units, and standard assumptions.
  • Structure answers with labeled diagrams, concise bullet points, and highlight final answers in numerical solutions.
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Curriculum Syllabus & Marking Scheme