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 Double Phospho/Dephosphorylation Cycle as a Benchmark to Validate an Effective Taylor Series Method to Integrate Ordinary Differential Equations

Symmetry ◽  
2021 ◽  
Vol 13 (9) ◽  
pp. 1684
Author(s):  
Alessandro Borri ◽  
Francesco Carravetta ◽  
Pasquale Palumbo
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Taylor Series ◽  
Enzymatic Reactions ◽  
Model Simplification ◽  
Stiff Ordinary Differential Equations ◽  
State Approximation ◽  
Steady State Approximation ◽  
Taylor Series Method ◽  
Taylor Series Methods

The double phosphorylation/dephosphorylation cycle consists of a symmetric network of biochemical reactions of paramount importance in many intracellular mechanisms. From a network perspective, they consist of four enzymatic reactions interconnected in a specular way. The general approach to model enzymatic reactions in a deterministic fashion is by means of stiff Ordinary Differential Equations (ODEs) that are usually hard to integrate according to biologically meaningful parameter settings. Indeed, the quest for model simplification started more than one century ago with the seminal works by Michaelis and Menten, and their Quasi Steady-State Approximation methods are still matter of investigation nowadays. This work proposes an effective algorithm based on Taylor series methods that manages to overcome the problems arising in the integration of stiff ODEs, without settling for model approximations. The double phosphorylation/dephosphorylation cycle is exploited as a benchmark to validate the methodology from a numerical viewpoint.

scholarly journals Generalized Taylor Series Method for Solving Nonlinear Fractional Differential Equations with Modified Riemann-Liouville Derivative

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
Süleyman Öğrekçi
Keyword(s):  
Differential Equations ◽  
Taylor Series ◽  
Nonlinear Differential Equations ◽  
Simple Algorithm ◽  
Series Method ◽  
Nonlinear Functions ◽  
Generalized Taylor Series ◽  
Liouville Derivative ◽  
Taylor Series Method ◽  
Generalized Differential

We propose an efficient analytic method for solving nonlinear differential equations of fractional order. The fractional derivative is defined in the sense of modified Riemann-Liouville derivative. A new technique for calculating the generalized Taylor series coefficients (also known as “generalized differential transforms,” GDTs) of nonlinear functions and a new approach of the generalized Taylor series method (GTSM) are presented. This new method offers a simple algorithm for computing GDTs of nonlinear functions and avoids massive computational work that usually arises in the standard method. Several illustrative examples are demonstrated to show effectiveness of the proposed method.

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