Course Title: 
Software Based Numerical Computation Methods
Course Code: 
Year Taught: 
Postgraduate (PG)
School of Engineering

'Software Based Numerical Computation Methods' is a course offered in the M. Tech. in Power & Energy Engineering program at School of Engineering, Amrita Vishwa Vidyapeetham, Amritapuri campus.

Solution of equations and Eigen value problems: linear interpolation methods, method of false position, Newton’s method, statement of fixed point theorem, fixed point iteration, solution of linear system by Gaussian elimination, LU decomposition and partial pivoting, Gauss-Jordon method and iterative methods, inverse of a matrix by Gauss Jordon method, Eigen value of a matrix by power method, Simulation/case study in short circuit analysis. Initial value problems for ordinary differential equations: single step methods, Taylor series method, Euler and modified Euler methods, fourth order Runge - Kutta method for solving first and second order equations, Simulation/case study in transient stability analysis, midterm stability analysis, etc. Linear programming: Formulation, graphical and simplex methods, Big-M method. Regression & interpolation: linear least squares regression, functional and nonlinear regression, Simulation/case study in state estimation, optimal power flow, etc. Unconstrained one dimensional optimization techniques: Necessary and sufficient conditions. Unrestricted search methods: quadratic interpolation methods, cubic interpolation and direct root methods. Unconstrained n- dimensional optimization techniques: Direct search methods, random search, descent methods, steepest descent, conjugate gradient, Simulation. Constrained optimization techniques: necessary and sufficient conditions, equality and inequality constraints, Kuhn-Tucker conditions, penalty function method, Simulation/Case study in economic operation of power systems. Dynamic programming, principle of optimality, recursive equation approach, application to shortest route, cargo-loading, allocation and production schedule problems, Simulation/case study in transmission system expansion. Practice session: Simulation and coding of different computational methods as mentioned above.

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  • S. S. Rao, “Engineering Optimisation Theory and Practice”, John Wiley and Sons, 2009.
  • Taha H. A., “Operations Research – An Introduction”, Prentice Hall of India, Eighth Edition, 2008.
  • Gerald C. F. and Wheatley P. O, “Applied Numerical Analysis”, Sixth Edition, Pearson Education Asia, New Delhi, 2002.
  • Fausett L. V. "Applied Numerical Analysis using MATLAB" Pearson Education Second Edition..
  • S.A. Soman, S.A. Khaparde, Shubha Pandit, " Computational Methods for Large Sparse Power Systems Analysis: An Object Oriented Approach Power Electronics and PowerSystems", Springer Science & Business Media, 2012.
  • Mariesa L. Crow, “Computational Methods for Electric Power Systems", CRC Press, 2015.