Applied Numerical Mathematics

This book gathers selected, peer-reviewed contributions presented at the Fifth International Conference on Numerical Analysis and Optimization (NAO-V), which was held at Sultan Qaboos University, Oman, on January 6-9, 2020. Each chapter reports on developments in key fields, such as numerical analysis, numerical optimization, numerical linear algebra, numerical differential equations, optimal control, approximation theory, applied mathematics, derivative-free optimization methods, programming models, and challenging applications that frequently arise in statistics, econometrics, finance, physics, medicine, biology, engineering and industry.

This book is intended to make recent results on the derivation of higher order numerical schemes for random ordinary differential equations (RODEs) available to a broader readership, and to familiarize readers with RODEs themselves as well as the closely associated theory of random dynamical systems. In addition, it demonstrates how RODEs are being used in the biological sciences, where non-Gaussian and bounded noise are often more realistic than the Gaussian white noise in stochastic differential equations (SODEs).

This book deals with various aspects of scientific numerical computing. No at­ tempt was made to be complete or encyclopedic. The successful solution of a numerical problem has many facets and consequently involves different fields of computer science. Computer numerics- as opposed to computer algebra- is thus based on applied mathematics, numerical analysis and numerical computation as well as on certain areas of computer science such as computer architecture and operating systems. Applied Mathemalies I I I Numerical Analysis Analysis, Algebra I I Numerical Computation Symbolic Computation I Operating Systems Computer Hardware Each chapter begins with sample situations taken from specific fields of appli­ cation. Abstract and general formulations of mathematical problems are then presented. Following this abstract level, a general discussion about principles and methods for the numerical solution of mathematical problems is presented. Relevant algorithms are developed and their efficiency and the accuracy of their results is assessed. It is then explained as to how they can be obtained in the form of numerical software. The reader is presented with various ways of applying the general methods and principles to particular classes of problems and approaches to extracting practically useful solutions with appropriately chosen numerical software are developed. Potential difficulties and obstacles are examined, and ways of avoiding them are discussed. The volume and diversity of all the available numerical software is tremendous.