Mathematical Methods, Modelling and Applications

• Other Authors: Jódar, Lucas (Editor), Company, Rafael (Editor)
• Format: Electronic Book Chapter
• Language: English
• Published: Basel MDPI - Multidisciplinary Digital Publishing Institute 2022
• Subjects: Research & information: general; Mathematics & science; mathematical modeling; infiltration well; differential equations; porous medium; fractal conductivity model; incomplete rankings; Kendall's tau; permutation graph; competitive balance; Spotify; collocation; volterra integral equation; highly oscillatory; convergence; areal porosity; volumetric porosity; fractal area-volume relationship; tortuosity factor; joint probability; corrugated box printing machine; modified Delphi method; analytic network process (ANP); supplier; nonlinear system; iterative method; divided difference operator; stability; parameter plane; dynamical plane; random hyperbolic model; random laplace transform; numerical integration; monte carlo method; numerical simulation; talbot algorithm; stochastic perturbations; random nonlinear oscillator; maximum entropy principle; probability density function; stationary Gaussian noise; random mean square parabolic model; finite degree of randomness; random finite difference scheme; relativistic harmonic oscillator; kinematics of a particle; special relativity; nonlinear problems in mechanics; equations of motion in gravitational theory; virus propagation; stochastic modeling; Gillespie algorithm; conservative formulation; multidimensional fragmentation equation; weight functions; finite volume scheme; contamination plume; advection-diffusion; universal curves; Dirichlet-to-Neumann map; Schrödinger operator; contagion effect; difference equation; elections; labor condition; mathematical compartmental discrete model; political corruption; revolving doors; sensitivity analysis; simulation; numerical methods; integro-interpolation method; splitting method; convergence of models; standard deviation of the error; diabetic retinopathy; ocular fundus; laser coagulation; optical coherence tomography; image processing; segmentation; safe treatment; Hermite interpolation; nodal systems; unit circle; circular membrane; fluid-structure interaction; differential-integral equations; power series method; closed-form solution; time series model; wavelet transform; ARIMA model; neural network NARX; ionospheric parameters; courtyard; climate change; microclimate; Support Vector Regression (SVR); machine learning; matrix functions; matrix hyperbolic tangent; matrix exponential; Taylor series; matrix polynomial evaluation; n/a
• Online Access: DOAB: download the publication; DOAB: description of the publication

This volume deals with novel high-quality research results of a wide class of mathematical models with applications in engineering, nature, and social sciences. Analytical and numeric, deterministic and uncertain dimensions are treated. Complex and multidisciplinary models are treated, including novel techniques of obtaining observation data and pattern recognition. Among the examples of treated problems, we encounter problems in engineering, social sciences, physics, biology, and health sciences. The novelty arises with respect to the mathematical treatment of the problem. Mathematical models are built, some of them under a deterministic approach, and other ones taking into account the uncertainty of the data, deriving random models. Several resulting mathematical representations of the models are shown as equations and systems of equations of different types: difference equations, ordinary differential equations, partial differential equations, integral equations, and algebraic equations. Across the chapters of the book, a wide class of approaches can be found to solve the displayed mathematical models, from analytical to numeric techniques, such as finite difference schemes, finite volume methods, iteration schemes, and numerical integration methods.