A modified taylor series method for solving initial-value problems in ordinary differential equations

1997 ◽  
Vol 65 (3-4) ◽  
pp. 231-246 ◽  
Author(s):  
F. Reverter ◽  
J. M. Oller
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Taylor Series ◽  
Initial Value Problems ◽  
Series Method ◽  
Initial Value ◽  
Taylor Series Method

scholarly journals Model of the telegraph line and its numerical solution

2018 ◽  
Vol 8 (1) ◽  
pp. 10-17 ◽  
Author(s):  
Petr Veigend ◽  
Gabriela Nečasová ◽  
Václav Šátek
Keyword(s):  
Differential Equations ◽  
Numerical Solution ◽  
Ordinary Differential Equations ◽  
Taylor Series ◽  
Variable Step Size ◽  
Time Interval ◽  
Variable Order ◽  
Series Method ◽  
Linear Solver ◽  
Taylor Series Method

Abstract This paper deals with a model of the telegraph line that consists of system of ordinary differential equations, rather than partial differential telegraph equation. Numerical solution is then based on an original mathematical method. This method uses the Taylor series for solving ordinary differential equations with initial condition - initial value problems in a non-traditional way. Systems of ordinary differential equations are solved using variable order, variable step-size Modern Taylor Series Method. The Modern Taylor Series Method is based on a recurrent calculation of the Taylor series terms for each time interval. The second part of paper presents the solution of linear problems which comes from the model of telegraph line. All experiments were performed using MATLAB software, the newly developed linear solver that uses Modern Taylor Series Method. Linear solver was compared with the state of the art solvers in MATLAB and SPICE software.

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.

A Multiple Interval Chebyshev-Gauss-Lobatto Collocation Method for Ordinary Differential Equations

2016 ◽  
Vol 9 (4) ◽  
pp. 619-639 ◽  
Author(s):  
Zhong-Qing Wang ◽  
Jun Mu
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Collocation Method ◽  
Initial Value Problems ◽  
Numerical Experiments ◽  
High Order Accuracy ◽  
Nonlinear Ordinary Differential Equations ◽  
Initial Value ◽  
Order Accuracy ◽  
Long Time

AbstractWe introduce a multiple interval Chebyshev-Gauss-Lobatto spectral collocation method for the initial value problems of the nonlinear ordinary differential equations (ODES). This method is easy to implement and possesses the high order accuracy. In addition, it is very stable and suitable for long time calculations. We also obtain thehp-version bound on the numerical error of the multiple interval collocation method underH1-norm. Numerical experiments confirm the theoretical expectations.

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