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ŠMARDA, Z. KOROBKO, E. VYROUBALOVÁ, J.
Original Title
Semi-analytical Numerical Methods
Type
course reader
Language
English
Original Abstract
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.
Keywords
Differential equations
Authors
ŠMARDA, Z.; KOROBKO, E.; VYROUBALOVÁ, J.
Released
22. 5. 2023
Pages from
1
Pages to
71
Pages count
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" }