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3 Silesian Journal of Pure and Applied Mathematics

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Application of the Taylor differential transformation for solving the integro-differential equations

Grzymkowski R., Pleszczyński M.

Silesian Journal of Pure and Applied Mathematics

2018

Vol. 8, iss. 1

33--48

A method of solving the integro-differential equations is presented. The discussed equations will be solved by the Taylor differential transformation. By using appropriate properties of this transformation the integro-differential equation will be transformed to a respective recurrence equation. Unfortunately, the high degree of generality and complexity of such defined problem does not allow to obtain the solution in general form. Each equation requires a special method of solution.

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.