Chapter 1: Recent Innovations and Advances in Mathematical Modeling for Engineering Systems Chapter 2: A Study of Approximation Techniques used to Solve Queueing Models that Arise in Optimizing Complex Engineering Systems Chapter 3: Stochastic Modeling in Engineering Systems: A study of a Nuclear Power Plant System Chapter 4: Nonlinear Dynamics and Chaos in Engineering Systems: Through an Epidemic Model Chapter 5: Eco-epidemiological Analysis of Plant-Herbivore Interactions: The Allee Effect and Time-dependent Dynamics Chapter 6: Impacts of Pesticides and External Interventions on Crop Production: A Modeling Approach Chapter 7: Tensor Foundations of Tunnel Mathematics Chapter 8: Boundary Element Analysis for MHD Stokes Flow through a Microchannel Exhibiting Surface Roughness Chapter 9: Numerical Investigation of Non-Darcy MHD Boundary Layer Nanofluids Flow Over a Non-linear Stretching Surface Chapter 10 : Extended Hydrodynamic Models for Rayleigh-Brillouin Scattering in Polyatomic Rarefied Gases: A Comparative Study Chapter 11: Nodal Discontinuous Galerkin Framework for Solving Grad-17 Moment Equations in a Rarefied Regime Chapter 12: Exploring the Method of Fundamental Solutions for Nonhomogeneous and Nonlinear Partial Differential Equations Chapter 13: A Fractional order Taylor Wavelets Approach for the Numerical Simulation of Fractional Variational Problems Chapter 14: New Fourth-order Efficient Numerical Solutions of the Klein-Gordon Equation Chapter 15: Numerical Approximation of the Sine-Gordon Equation by Using the Hybrid B-spline Differential Quadrature Method Chapter 16: An Overview of High-resolution Schemes in the OpenFOAM Toolkit