Semi-analytical Numerical Methods

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.