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SESSION Nov-dec2023
course CODE & NAME DCA2101 & Computer Oriented Numerical Methods













  1. Show that





Ans 1.

To prove the given identities, let’s start by defining the operators:

= Laplacian operator (also known as the second-order spatial derivative operator)

= Gradient operator (vector of first-order spatial derivatives)

Divergence operator (divergence of a vector field)



  1. b) To prove :

Let’s start with the left-hand side (LHS):

Using the definitions of the Laplacian  and gradient  operators, we have:

Expanding the terms, we can

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  1. Solve the system of equation by Gauss Elimination’s method







Ans 2.


Consider the given system of equations,





Convert the system to matrix form,


The augmented matrix for the above matrix form,



Q3. Find the equation of the best fitting straight line for the data:


X 1 3 4 6 8 9 11 14
Y 1 2 4 4 5 7 8 9



Ans 3.

To find the equation of the best-fitting straight line for the given data points, you can use linear regression. The equation of a straight line is typically represented as:

Y = mx + b


  • Y is the dependent variable (in this case, the Y values).
  • X is the independent variable (in this case, the X values).
  • m is the






Q4. Evaluate f(15), given the following table of values:


x 10 20 30 40 50
y = f(x) 46 66 81 93 101


Ans 4.

To evaluate f(15) using the given table of values, you can use interpolation. Since the table provides values of y = f(x) for specific values of x, you can interpolate to find the value of f(15) which falls between x = 10 and x = 20.

We can use linear interpolation for this purpose. Linear interpolation assumes that the function f(x) varies linearly between two data points. Here’s how you can calculate f(15):

First, identify the two data





Q5. Use Taylor’s series method to solve the initial value problem:

 for   given that .



Ans 5.


The Differential Equation

With initial condition


  1. Apply Runge-Kutta fourth order method to find an approximate value of y when x = 0.1 given that , .


Ans 6.

To apply the Runge-Kutta fourth-order method to solve the given initial value problem, we need to follow these steps:

  1. Define the differential equation:
  2. Specify the initial