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Application of the Taylor differential transformation in the calculus of variations

Grzymkowski R., Pleszczyński M., Hetmaniok E.

Silesian Journal of Pure and Applied Mathematics

2017

Vol. 7, iss. 1

65--82

The paper presents the method of solving some problems belonging to the area of the calculus of variations, that is the problems of searching for the selected types of functionals which can be transformed to some, nonlinear in general, ordinary differential equations or systems of such equations. The obtained equations are solved on the basis of the Taylor differential transformation.

The Taylor transformation hybrid method applied for solving the Stefan problem

Grzymkowski R., Hetmaniok E., Pleszczyński M.

Silesian Journal of Pure and Applied Mathematics

2016

Vol. 6, iss. 1

111--123

The paper presents the analytic-numerical hybrid method using, among others, the Taylor transformation, thanks to which the solution of the Stefan problem is replaced by the solution of a nonlinear system of equations.