This book highlights the work of several world-class researchers on smart modeling of complex systems. The contributions are grouped into the four main categories listed below. ·         Numerical schemes construction for the solution of partial differential equations. ·         Numerical methods in continuum media mechanics problems. ·        Mathematical modeling in aerodynamics, plasma physics, deformable body mechanics, and geological hydrocarbon exploration. ·         Mathematical modeling in medical applications. The book offers a valuable resource for theoreticians and application scientists and engineers, as well as postgraduate students, in the fields of computational methods, numerical experiments, parallel algorithms, deformable solid bodies, seismic stability, seismic prospecting, migration, elastic and acoustic wave investigation, gas dynamics, astrophysics, aerodynamics, fluid dynamics, turbulent flows, hypersonic flows, detonation waves, composite materials, fracture mechanics, melting of metals, mathematical economics, medicine, and biology.