scholarly journals A Program for the Automatic Integration of Differential Equations using the Method of Taylor Series

1960 ◽  
Vol 3 (2) ◽  
pp. 108-111 ◽  
Author(s):  
A. Gibbons
Keyword(s):  
Differential Equations ◽  
Taylor Series ◽  
Automatic Integration

A simple analytical approach to a nonlinear equation arising in porous catalyst

2017 ◽  
Vol 27 (4) ◽  
pp. 861-866 ◽  
Author(s):  
Chun-Hui He
Keyword(s):  
Differential Equations ◽  
Nonlinear Equation ◽  
Taylor Series ◽  
Analytical Approach ◽  
Nonlinear Differential Equations ◽  
Solution Process ◽  
Content Type ◽  
Porous Catalyst ◽  
Taylor Series Method ◽  
Heat And Fluid Flow

Purpose Analytical methods are widely used in heat and fluid flow; the purpose of this paper is to couple Taylor series method and Bubbfil algorithm to solve nonlinear differential equations. Design/methodology/approach A series solution is obtained with some unknown constants, which can be determined by incorporating boundary conditions, and the constants are calculated by the Bubbfil algorithm. Findings This paper gives an analytical approach to a nonlinear equation arising in porous catalyst using Taylor series and Bubbfil algorithm, and a high accuracy can be achieved. Research limitations/implications The coupled method of Taylor series and Bubbfil algorithm is a powerful method for nonlinear differential equations. Practical implications The proposed technology can be used in various numerical methods. Originality/value A new analytical method is proposed based on Taylor series and Bubbfil algorithm, which is a development of Newton’s iteration method and an ancient Chinese algorithm. The solution process is simple and easy to follow.

scholarly journals Multi-point Taylor series to solve differential equations

2019 ◽  
Vol 12 (6) ◽  
pp. 1791-1806 ◽  
Author(s):  
Djédjé Sylvain Zézé ◽  
◽  
Michel Potier-Ferry ◽  
Yannick Tampango ◽  
◽  
...  
Keyword(s):  
Differential Equations ◽  
Taylor Series

DERIVATION OF 2-POINT ZERO STABLENUMERICAL ALGORITHM OF BLOCK BACKWARD DIFFERENTIATION FORMULA FOR SOLVING FIRST ORDER ORDINARY DIFFERENTIAL EQUATIONS

2021 ◽  
Vol 5 (2) ◽  
pp. 579-583
Author(s):  
Muhammad Abdullahi ◽  
Bashir Sule ◽  
Mustapha Isyaku
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Taylor Series ◽  
Taylor Series Expansion ◽  
Order Ordinary Differential Equation ◽  
Differentiation Formula ◽  
First Order ◽  
Backward Differentiation Formula

This paper is aimed at deriving a 2-point zero stable numerical algorithm of block backward differentiation formula using Taylor series expansion, for solving first order ordinary differential equation. The order and zero stability of the method are investigated and the derived method is found to be zero stable and of order 3. Hence, the method is suitable for solving first order ordinary differential equation. Implementation of the method has been considered

scholarly journals Nonlinear Klein-Gordon and Schrödinger Equations by the Projected Differential Transform Method

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Younghae Do ◽  
Bongsoo Jang
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Taylor Series ◽  
Nonlinear Partial Differential Equations ◽  
Differential Transform Method ◽  
Schrödinger Equations ◽  
Partial Differential ◽  
Transform Method ◽  
Differential Transform ◽  
Klein Gordon

The differential transform method (DTM) is based on the Taylor series for all variables, but it differs from the traditional Taylor series in calculating coefficients. Even if the DTM is an effective numerical method for solving many nonlinear partial differential equations, there are also some difficulties due to the complex nonlinearity. To overcome difficulties arising in DTM, we present the new modified version of DTM, namely, the projected differential transform method (PDTM), for solving nonlinear partial differential equations. The proposed method is applied to solve the various nonlinear Klein-Gordon and Schrödinger equations. Numerical approximations performed by the PDTM are presented and compared with the results obtained by other numerical methods. The results reveal that PDTM is a simple and effective numerical algorithm.

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