arXiv subjects

Denys Dragunov

Publications and source records attributed to Denys Dragunov.

3 recordsLinked to original sources

arXiv2021

A transformation-based approach for solving stiff two-point boundary value problems

A new approach for solving stiff boundary value problems for systems of ordinary differential equations is presented. Its idea essentially generalizes and extends that from arXiv:1601.04272v8. The approach can be viewed as a methodology framework that allows to enhance "stiffness resistance" capabilities of pretty much all the known numerical methods for solving two-point BVPs. The latter is demonstrated on the example of the {\it trapezoidal scheme} with the corresponding C++ source code available at \url{https://github.com/imathsoft/MathSoftDevelopment}. Results of numerical experiments are provided to support the theoretical conclusions.

math.NA↗

arXiv2020

SI-method for solving stiff nonlinear boundary value problems

The paper contains a thorough theoretical analysis of the SI-method, which was firstly introduced in arXiv:1601.04272v8 and proved to be remarkably stable and efficient when applied to some instances of stiff boundary value problems (like the Troesch's problem). By suggesting a more general view on the SI-method's idea and framework, we managed to obtain sufficient conditions for the method to be applicable to a certain class of two-point boundary value problems. The corresponding error estimates are provided. Special attention is devoted to the exploration of the method's capabilities via a set of numerical examples. The implementation details of the method are discussed in fair depth. An open-source C++ implementation of the SI-method is freely available at the public repository https://github.com/imathsoft/MathSoftDevelopment.

math.NA↗

arXiv2013

Exponentially convergent numerical-analytical method for solving eigenvalue problems for singular differential operators

The article develops and proves an exponentially convergent numerical-analytical method (the FD-method) for solving Sturm-Liouville problems with a singular Legendre operator and a singular potential. Obtained within are sufficient conditions for convergence of the method and a priori estimates of its accuracy. A detailed algorithm for programmatic implementation of the FD-method is presented and compared with known algorithms (SLEIGN2).

math.NA↗