Manuscript Topics

Description: Since the early stages of modern science, researchers have been striving to capture the essence of complex natural phenomena by means of mathematical models, that often are expressed as systems of mixed non-linear, differential-algebraic equations. Generally, such mathematical models are overly complicated and their solutions in closed form appears to be unattainable. It is to be underlined that, in spite of decades of efforts, the mere existence of solutions for some mathematical models is yet unknown, as is the case for the Navier-Stokes equations. The inception of computer systems in scientific research practice, paired to fast-paced advancements in the development of numerical simulation algorithms, has substantially improved the qualitative and quantitative understanding of complex Mathematical models and of the physical phenomena that such models try to capture.

The present special issue of AIMS Mathematics, titled "Mathematical modeling and numerical simulation in science", aims at offering a scientific venue to researchers in theoretical as well as applied sciences and engineering to showcase recent advancements in the mathematical modeling of scientific phenomena and technological products. In addition, this special issue aims at offering an application-oriented venue to scientific efforts towards the numerical simulation of complex phenomena and technological products. Last but not least, contributions on the generalization of well-known mathematical models are sought, which are aimed at broadening the understanding of well-established physical theories that only partially match the known reality.

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