Theory of Algorithms and Computational Methods. Functions Approximations, Numerical Differentiation and Integration (Educational Tasks and Methodological Recommendations)

Kalnibolotsky, Y.M. and Melnik, (R.)V.N.

KPI Academic Publishers, 1990, 120 pages

About this book:

This book is for students who would like to acquire practical skills in the methodology of computational experiment - a powerful tool in solving engineering and science problems. The authors assume that the choice of a physical approximation for the given problem as well as the formulation of a mathematical model has already been made. In other words, it is assumed that a mathematical model of the process or phenomenon under consideration has already been constructed. Hence, in this textbook, they focus on the subsequent stages of the computational experiment: (a) design of an efficient  numerical method for the solution of the problem (design of a computational algorithm); (b) creating a computer code which implements that method (algorithm); (c) carrying out computations and the analysis of the numerical results obtained. The authors emphasize that after the last stage, it may be necessary to carry out a refinement of the mathematical model that has been used to study the process or phenomenon and to repeat the technological cycle of the computational experiment with the new, refined mathematical model. Each topic presented by the authors is accompanied by computational codes written in FORTRAN.  Along with the actual algorithms and computational codes, students will find all the necessary theoretical material covering two topics in numerical methods: functions approximations and numerical differentiation and integration.

This book is addressed mainly to undergraduate 3rd year students in engineering, mathematics, and sciences.