The literature reveals that numerous real-life phenomena in the subjects of physics and engineering which are governed by highly nonlinear Partial differential equations (PDEs) with unknown analytical solutions. More precisely, the (PDEs) arise in a wide variety of physical problems such as; by way of example not exhaustive enumeration, fluid dynamics, engineering mathematics, electrostatics, plasma physics, solid mechanics, chemistry, quantum field theory, bio-mathematics, etc. Therefore, such (PDEs) have received a huge attention from mathematicians, physicists, and engineers for the sake of approximating their analytical solutions. We aimed in this special issue to publish articles focusing on recent advanced numerical studies on Differential Equations related to physics and engineering. The well-developed analysis of existing numerical algorithms in terms of efficiency, applicability, convergence, stability and accuracy is of importance. A discussion of nontrivial numerical examples is encouraged.