 COURSE SUMMARY
Course Title:
Software Based Numerical Computation Methods
Course Code:
18MA608
Year Taught:
2018
Semester:
1
Degree:
School:
School of Engineering
Campus:
Amritapuri

'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.

#### SYLLABUS

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.

#### TEXT BOOKS / REFERENCES

• Fox R. L., “Optimization Methods for Engineering Design”, Addition Wesley, 1971.
• 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.