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RUDN mathematicians have created a software package for solving nonlinear differential equations

RUDN mathematicians have created a software package for solving nonlinear differential equations

RUDN mathematicians have created a universal package of computer programs for the study and solution of complex nonlinear differential equations and their systems. The development will be useful for hydrodynamics, gas dynamics, mechanics, elementary particle physics, plasma physics and elasticity theory. The article was published in the journal Computer Physics Communications.

Many processes in physics are mathematically described by partial differential equations — for example, string vibrations or heat transfer from one part of a solid to another. RUDN mathematicians have created a package of tools for the analysis of such equations and their systems. Previously, triangular decomposition methods were used to solve such differential equations: a complex equation was sequentially divided into simpler parts. The authors took a different approach - the Thomas decomposition method. During the tests, he showed superiority over previously used methods.

RUDN mathematicians also gave examples of application of the software package in practice by solving the Navier-Stokes and Burgers equations for an incompressible fluid that underlies hydrodynamics 

The software of RUDN mathematicians will expand the base of existing algorithms and simplify the work of specialists in physics, physical chemistry and information technology. The created tool package will help to find solutions of differential equations and their systems faster and with greater accuracy compared to previously existing methods.
 

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