|Numerical Methods & Computational Techniques||Learning Schedule|
Numerical methods are extremely powerful problem solving tools .These tools are capable of handling large system of equations, nonlinearities and complicated geometries that are not uncommon in engineering practice and that are often impossible to solve analytically. Numerical methods are an efficient vehicle for learning to use computer. Numerical solution of differential equations (Ordinary as well as Partial), that are often encountered when a dynamic system is modeled, is explained with special emphasis on standard equations such as heat equation, wave equation and Laplace equation. The practice session in computer Lab gives students an opportunity to learn the development of the code in C/C++ for implementation of these methods on a variety of problems.
To enhance problem solving skills of engineering students using a powerful problem solving tool namely numerical methods. The tool is capable of handling large systems of equations, nonlinearities and complicated geometries that are common in engineering practice but often impossible to solve analytically.
On completion of this course, the students will be able to
- Apply various numerical methods and appreciate a trade off in using them.
- Understand the source of various types of errors and their effect in using these methods.
- To distinguish between Numerical and Analytical methods along with their Merits and demerits.
- Understand the use of digital computers in implementation of these methods.
- Develop a code in C/C++ for the solution of problems that may not be solved by analytical methods.
Non- Linear Equations and system of Linear Equations: Introduction, error and error propagation, Bisection method, False position Method, Method of Iteration, Newton-Raphson Method, Secant Method, Gauss Elimination method Gauss – Jordan method, Gauss – Seidel method, convergence of iterative methods.
Interpolation: Newton’s Forward and Backward Interpolation, Lagrange’s Interpolation, Newton’s Divided Difference Interpolation, Inverse Interpolation.
Numerical Differentiation and Integration: Derivations from difference tables, Higher order derivations. Newton – Cotes integration formula, Trapezoidal rule, Simpson’s rule, Boole’s rule and Weddle’s rule, Romberg’s Integration.
Numerical Solution of Ordinary: Taylor series method, Euler and modified Euler method, Runge Kutta methods, Milne’s method, Finite Difference method.
Partial Differential Equations: Finite difference approximations of partial derivatives, Solution of Laplace’s equation (Elliptic) by iteration method, Solution of one dimensional heat equation (Parabolic) by Bender-Schmidt method and Crank – Nicolson method, Von-Neumann stability condition, Solution of one dimensional wave equation (Hyperbolic), CFL stability condition.
- Xavier: C Language and Numerical Methods.
- Dutta & Jana: Introductory Numerical Analysis.
- B.Scarborough: Numerical Mathematical Analysis.
- Jain, Iyengar ,& Jain: Numerical Methods (Problems and Solution).
- Balagurusamy: Numerical Methods, Scitech.
- Baburam: Numerical Methods, Pearson Education.
- Dutta: Computer Programming & Numerical Analysis, Universities Press.
- SoumenGuha& Rajesh Srivastava: Numerical Methods, OUP.