Numerical Methods and Computer Programming

This book focuses mainly on numerical method envisaged in almost every field of science and engineering and essentially in any type of work that requires calculations to give precise solutions. The point of numerical analysis is to analyze methods that are used to give approximate number solutions to situations where it is unlikely to find the real solution quickly and to try and improve upon these methods so as to reduce the amount of error generated by computer calculation. The book has embed in its contents the use of computing programming describe algorithmic solutions whose basic ideas are common to a variety of mathematical problems. By means of the methods presented, the reader will acquire the skills besides a fundamental knowledge to successfully work on related subjects in this field. Computing approach enables solution of complex problems with a great number of very simple operations.

Solution of Algebraic and Transcendental Equation: Introduction. Methods for Finding Root of an Equation. Order or Rate of Convergence. Newton-Raphson Method. Method for Complex Root. Lin- Bairstow Method. Graeff’s Root Square Method. Comparison. Newton-Raphson Method Program Code in C Language. Newton-Raphson Method MATLAB Code. Graeffe’s Root Squaring Method Program in C Language. Interpolation and Approximation: Introduction. Lagrange’s Interpolation Formula. Newton-Divided Difference Formula. Newton Interpolation Formula for Finite Differences. Cubic Spline. Least Squares Approximation using Chebyshev Polynomial. Solution of Linear Simultaneous Equation: Introduction. Cholesky’s (Crout’s) Method. LU Factorization. Iterative Method for Solution of Simultaneous Linear Equation. Numerical Differentiation and Integration: Introduction. Numerical Differentiation. Numerical Integration. Solution of Differential Equation: Introduction. Modified Euler’s Method. Runge-Kutta Method of Second Order. Runge-Kutta Method of Third Order. Runge-Kutta Method of Forth Order.Milne’s Predictor-Corrector Method. Stability of Ordinary Differential Equation. Index.