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Nonclassical symmetries of polynomial equations and test problems with parameters for computer algebra systems
Inna K. Shingareva, Andrei D. Polyanin
Nonclassical symmetries and reductions of polynomial equations and systems of polynomial equations are considered. It is shown that specific polynomial equations having "hidden" sy…
Notes on symmetries and reductions of algebraic equations
Inna K. Shingareva, Andrei D. Polyanin
Symmetries and reductions of some algebraic equations are considered. Transformations that preserve the form of several algebraic equations, as well as transformations that reduce…
Numerical integration of blow-up problems on the basis of non-local transformations and differential constraints
Andrei D. Polyanin, Inna K. Shingareva
Several new methods of numerical integration of Cauchy problems with blow-up solutions for nonlinear ordinary differential equations of the first- and second-order are described. S…
New numerical methods for blow-up problems
Andrei D. Polyanin, Inna K. Shingareva
Two new methods of numerical integration of Cauchy problems for ODEs with blow-up solutions are described. The first method is based on applying a differential transformation, wher…