by Jovan Pehcevski
This book covers topics from
numerical and symbolic computing, including the main numerical and
symbolic methods, schemes and applications. Section 1 focuses on
numerical computing methods, describing matrix differential equations
for solving systems of linear algebraic equations, a numerical problem
encryption for high-performance computing applications, a numerical
verification method of solutions for elliptic variational inequalities,
a trigonometric numerical integrator for solving first order ordinary
differential equation, and augmented Lagrangian methods for numerical
solutions to higher order differential equations. Section 2 focuses on
symbolic computing methods, describing a learning network assisted by
means of symbolic computation, multiple factorial analysis of symbolic
data, combining symbolic tools with interval analysis, and application
to solve robust control problems, symbolic and graphical computations
of a class of slightly perturbed equations. Section 3 focuses on
numerical computing applications, describing non-negativity preserving
numerical algorithms for problems in mathematical finance, a continuum
approach using numerical simulations of microscale gas flows, numerical
methods in electro-cardiology, numerical simulation of the blood flow
through a brain vascular aneurysm with an artificial stent using the
SPH method, and numerical modeling of soil water flow and nitrogen
dynamics in a tomato field irrigated with municipal wastewater. Section
4 focuses on symbolic computing applications, describing symbolic time
series analysis and its application in social sciences, application of
symbolic computation in nonlinear differential-difference equations,
symbolic modelling of dynamic human motions, and a framework for
bridging the gap between symbolic and non-symbolic AI.
