Manuscript Topics
Most natural phenomena of Biosciences, Engineering and Social Sciences are modelled by differential equations, in particular, by nonlinear differential equations. It is for this reason that the scientific, mathematical, and engineering communities are more and more attracted to study differential equations and to look for their exact solutions. Exact solutions not only provide a proper understanding of the natural phenomena but they also allow one to test, meticulously and precisely, several approximate analytical and numerical methods for solving such equations. Due to the difficulty in finding exact solutions of differential equations, researchers are in constant pursuit of developing accurate and powerful numerical algorithms for simulation of solutions to such equations.

This Special Issue is focused on gathering original and innovative contributions on finding exact solutions to differential equations. Also, an extensive range of computational methods extending from efficient finite element and finite difference methods, multi-scale methods, adaptive methods to kinetic Monte Carlo simulations and spectral methods will be considered.

Possible contributions include but are not limited to:

• Closed-form solutions of differential equations of Mathematical Biosciences and Engineering
• traveling-wave and similarity solutions
• Lie group classification of ordinary and partial differential equations
• Conservation laws
• classical and nonclassical symmetries of differential equations
• variational analysis and dynamical systems
• wave-type and reaction–diffusion equations
• optimization and control theory
• development and analysis of new methods for numerical solution of PDEs

Instructions for authors
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Please submit your manuscript to online submission system
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