A Collocation Type Implicit Taylor Series Algorithm for ODE Initial Value Problems

2009 ◽  
Author(s):  
G. Molnárka ◽  
E. Miletics
Keyword(s):  
Taylor Series ◽  
Initial Value Problems ◽  
Initial Value

scholarly journals Taylor Series Based Numerical Integration Method

2020 ◽  
Vol 11 (1) ◽  
pp. 60-69
Author(s):  
Petr Veigend ◽  
Gabriela Nečasová ◽  
Václav Šátek
Keyword(s):  
Taylor Series ◽  
Initial Value Problems ◽  
Integration Method ◽  
Autonomous Systems ◽  
Nonlinear Problems ◽  
Numerical Integration Method ◽  
Initial Value ◽  
Matlab Implementation ◽  
Linear And Nonlinear ◽  
Positive Properties

AbstractThis article deals with a high order integration method based on the Taylor series. The paper shows many positive properties of this method on a set of technical initial value problems. These problems can be transformed into the autonomous systems of ordinary differential equations for both linear and nonlinear problems. The MATLAB implementation of the method is compared with state-ofthe-art MATLAB solvers.

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 Solving nonlinear and non-autonomous ODEs systems by the ADM using a new several-variables Adomian polynomials

2021 ◽  
Author(s):  
Idriss Noureddine Zaouagui ◽  
Toufik Badredine
Keyword(s):  
Taylor Series ◽  
Initial Value Problems ◽  
Decomposition Method ◽  
Differential Operators ◽  
Adomian Decomposition Method ◽  
Initial Value ◽  
Adomian Polynomials ◽  
Solution Series ◽  
Several Variables ◽  
Adomian Decomposition

In this work, we adapted another time the Adomian decomposition method for solving nonlinear and non-autonomous ODEs systems. Therefore, our expressions of the Adomian polynomials are determined for a several-variable differential operators. The solution series is shown that it stay coincide with the Taylor series. Thus new conditions of convergence have been established, some systemes has been solved by ADM using Maple 2020. keywords Adomian decomposition method, Adomian polynomials, ODEs systems, initial value problems, several-variables differential operators. Classification 26B12, 34L30, 47E05, 65B10, 65L05, 65L80

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