Course Title: Computational Physics

Programme: B Sc. Physics 

Semester: VI

Course Introduction:

Computational physics is the study and implementation of numerical analysis to solve problems in physics for which a quantitative theory already exists. Historically, computational physics was the first application of modern computers in science and is now a subset of computational science. Computational Physics can be considered as a subdiscipline of theoretical physics. It also establishes the bridge between theoretical Physics and experimental physics.

Course Objective 

This course covers various numerical methods for solving linear and nonlinear systems of equations, interpolation techniques, numerical differentiation, and integrations. The algorithm for all the numerical methods is covered in the course.  

Course Outcome:

After the successful completion of this course, a student would be able to 

1. Solve systems of equations(linear, nonlinear, and system of the linear equation ) using any method they learned. Students will become capable of selecting the optimal method for solving the system depending on the requirement. 
2. Perform interpolation using different techniques.
3. Find the function(linear, nonlinear, and exponential), which fit the given set of data
4. Perform numerical integration and differentiation using different techniques. Solve dynamics systems in physics using numerical techniques for which the analytical solution is difficult. 
5. Write algorithm for all the numerical techniques (outcomes: 1,2,3 and 4)
6. Write computer programmes for numerical methods as they learn algorithms for each method.

Syllabus:

Module I (18 hours)

Solutions of Nonlinear Equations

Bisection Method – Newton Raphson method (two-equation solution) – Regula-Falsi Method, Secant method – Fixed point iteration method – Rate of convergence and comparisons of these Methods

Solution of a system of linear algebraic equations

Gauss elimination method with pivoting strategies-Gauss-Jordan method-LU Factorization, Iterative methods (Jacobi method, Gauss-Seidel method)

Module II (18 hours)

Curve fitting: Regression and interpolation

Least-squares Regression- fitting a straight line, parabola, polynomial and exponential curve

Finite difference operators-forward differences, divided difference; shift, average and differential operators- Newton’s forward difference interpolation formulae- Lagrange interpolation polynomial- Newton’s divided difference interpolation polynomial

Module III (18 hours)

Numerical Differentiation and Integration

Numerical Differentiation formulae – Maxima and minima of a tabulated function- Newton- Cote general quadrature formula – Trapezoidal, Simpson’s 1/3, 3/8 rule.

Solution of ordinary differential equations

Taylor Series Method, Picard’s method-Euler’s and modified Euler’s method –Heun’s method- Runge Kutta methods for 1st and 2nd order

(Algorithms for all numerical methods should be covered)