Detail publikace

Semi-analytical Numerical Methods

ŠMARDA, Z. KOROBKO, E. VYROUBALOVÁ, J.

Originální název

Semi-analytical Numerical Methods

Typ

skriptum

Jazyk

angličtina

Originální abstrakt

This textbook is an additional study material to numerical methods for solution of ordinary differential equations (ODE), functional differential equations (FDE), partial differential equations (PDE) in subjects Selected Parts from Mathematics II. The goal of this textbook is to enhance students' knowledge in the area of semi-analytic methods for solution of ODE, FDE and PDE. Specifically, differential transformation method will be presented. In comparison to other semi-analytic methods like homotopy perturbation method, variational iteration method, Adomian decomposition method and homotopy analysis method, differential transformation method offers simple algebraic recurrent scheme which can be easily implemented without a need for symbolic calculations of derivatives or multidimensional integrals. The textbook is especially focused on differential transformation method and its applications in solution of initial value problems for singular initial value problems with nonlinearities, initial value problems for functional differential equations with proportional and/or constant delay. Moreover, in conclusion, we also present an efficient iterative method for PDE based on Cauchy integral formula.

Klíčová slova

Differential equations

Autoři

ŠMARDA, Z.; KOROBKO, E.; VYROUBALOVÁ, J.

Vydáno

22. 5. 2023

Strany od

1

Strany do

71

Strany počet

71

BibTex

@misc{BUT183565,
  author="Zdeněk {Šmarda} and Evgeniya {Korobko} and Jana {Vyroubalová}",
  title="Semi-analytical Numerical  Methods",
  year="2023",
  pages="1--71",
  note="course reader"
}