IMPLICIT EXTENSION OF TAYLOR SERIES METHOD FOR INITIAL VALUE PROBLEMS

2003 ◽  
Author(s):  
G. MOLNÁRKA
Keyword(s):  
Taylor Series ◽  
Initial Value Problems ◽  
Series Method ◽  
Initial Value ◽  
Taylor Series Method

scholarly journals The Taylor series method of order $p$ and Adams-Bashforth method on time scales

2021 ◽  
Author(s):  
Svetlin Georgiev ◽  
Inci Erhan
Keyword(s):  
Time Scales ◽  
Taylor Series ◽  
Initial Value Problems ◽  
Arbitrary Order ◽  
Trapezoidal Rule ◽  
Dynamic Equations ◽  
Series Method ◽  
Initial Value ◽  
Nonlinear Dynamic Equations ◽  
Taylor Series Method

A recent study on the Taylor series method of second order and the trapezoidal rule for dynamic equations on time scales has been continued by introducing a derivation of the Taylor series method of arbitrary order $p$ on time scales. The error and convergence analysis of the method is also obtained. The 2 step Adams-Bashforth method for dynamic equations on time scales is concluded and applied to examples of initial value problems for nonlinear dynamic equations. Numerical results are presented and discussed.

scholarly journals Estimates in the Taylor series method for polynomial total systems of PDEs

2021 ◽  
Vol 17 (1) ◽  
pp. 27-39
Author(s):  
Levon K. Babadzanjanz ◽  
◽  
Irina Yu. Pototskaya ◽  
Yulia Yu. Pupysheva ◽  
◽  
...  
Keyword(s):  
Cauchy Problem ◽  
Taylor Series ◽  
Series Method ◽  
Initial Value ◽  
Taylor Coefficients ◽  
Recurrence Formulas ◽  
The Cauchy Problem ◽  
Taylor Series Method ◽  
Systems Of Pdes ◽  
Ode Systems

Many of total systems of PDEs can be reduced to the polynomial form. As was shown by various authors, one of the best methods for the numerical solution of the initial value problem for ODE systems is the Taylor Series Method (TSM). In the article, the authors consider the Cauchy problem for the total polynomial PDE system, obtain the recurrence formulas for Taylor coefficients, and then formulate and prove a theorem on the accuracy of its solutions by TSM.

Multi-rate Integration and Modern Taylor Series Method

2008 ◽  
Author(s):  
Jirí Kunovský ◽  
Martina Drozdová ◽  
Jirí Petrek ◽  
Pavla Sehnalová ◽  
František Zboril
Keyword(s):  
Taylor Series ◽  
Series Method ◽  
Taylor Series Method
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