Textbook in PDF format This volume deals with recent research in the fields of pure and applied mathematics. Since numerical simulation plays a definitive role in theoretical and applied research, the book's topics are highly appreciated by pure research scientists, applied mathematicians, engineers, and post-graduate students who conduct research in applied science and beyond. Numerical simulation and modelling serve as a bridge, linking various numerical approaches to solving engineering problems with numerical data. This enables a better understanding of the studied processes or phenomena, leading to improved knowledge and the potential to develop mechanisms for managing them. A Case for the Application of Analytic Continuation in Physics Calculations of Flows with Deflagration Appearance in Channels with Obstacles Numerical Modeling Techniques to Solving Complex Geotechnical Problems: Case Studies On the 1-Parameter Trigonometric and Hyperbolic Inequalities Chains Random Processes Defined by Stochastic Differential and Difference Equations The Optimization Problems and Modeling the Radiation Characteristics of Focusing Radiating Array