Course Title: Computational Physics
Programme: B Sc. Physics
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.
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.
After the successful completion of this course, a student would be able to
- 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.
- Perform interpolation using different techniques.
- Find the function(linear, nonlinear, and exponential), which fit the given set of data
- Perform numerical integration and differentiation using different techniques. Solve dynamics systems in physics using numerical techniques for which the analytical solution is difficult.
- Write algorithm for all the numerical techniques (outcomes: 1,2,3 and 4)
- Write computer programmes for numerical methods as they learn algorithms for each method.
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)
Module 1 A. Solution to Nonlinear Equations
Module 1 B. Solution of System of Linear Algebraic Equations
Module 2. Curve fitting: Regression and interpolation
- Regression – Least squares – Straight Line
- Regression – Least Square – Power Function Model
- Regression – Least Square – Saturation Growth Rate Equation
- Regression – Least Square – Polynomial Fit
- Interpolation – Linear fit
- Interpolation – Lagrangian Interpolation polynomial
- Interpolation – Newton Interpolation Polynomial
- Interpolation – Divided Difference Table
- Interpolation – Gregory – Newton Interpolation Polynomial
- Interpolation – Newton-Gregory Backward Interpolation Polynomial
Module 3 A. Numerical Differentiation and Integration
Module 3 B. Solution of Ordinary Differential Equations