scholarly journals A New Iterative Method for Riccati Differential Equation

2017 ◽  
Vol V (XI) ◽  
pp. 2722-2725
Author(s):  
Shivaji Tate
Keyword(s):  
Differential Equation ◽  
Iterative Method ◽  
Riccati Differential Equation ◽  
New Iterative Method

scholarly journals By using a new iterative method to the generalized system Zakharov-Kuznetsov and estimate the best parameters via applied the pso algorithm

2020 ◽  
Vol 19 (2) ◽  
pp. 1055 ◽  
Author(s):  
Abeer Aldabagh
Keyword(s):  
Differential Equation ◽  
Exact Solution ◽  
Iterative Method ◽  
Numerical Method ◽  
Pso Algorithm ◽  
Accurate Solution ◽  
Generalized System ◽  
A New Technique ◽  
Best Parameters ◽  
New Iterative Method

In this paper, a new iterative method was applied to the Zakharov-Kuznetsov system to obtain the approximate solution and the results were close to the exact solution, A new technique has been proposed to reach the lowest possible error, and the closest accurate solution to the numerical method is to link the numerical method with the pso algorithm which is denoted by the symbol (NIM-PSO). The results of the proposed Technique showed that they are highly efficient and very close to the exact solution, and they are also of excellent effectiveness for treating partial differential equation systems.

scholarly journals An efficient new iterative method for oscillator differential equation

2012 ◽  
Vol 19 (6) ◽  
pp. 1473-1477 ◽  
Author(s):  
Yasir Khan ◽  
H. Vázquez-Leal ◽  
N. Faraz
Keyword(s):  
Differential Equation ◽  
Iterative Method ◽  
New Iterative Method

scholarly journals Modified New Iterative Method for Solving Nonlinear Partial Differential Equations

2020 ◽  
Vol 19 ◽  
pp. 1-10
Author(s):  
Alaa K. Jabber
Keyword(s):  
Differential Equation ◽  
Differential Operator ◽  
Iterative Method ◽  
Initial Value Problems ◽  
Linear Differential Operator ◽  
Nonlinear Partial Differential Equations ◽  
Initial Value ◽  
The Laplace Transform ◽  
Linear Differential ◽  
New Iterative Method

In this paper, the iterative method, proposed by Gejji and Jafari in 2006, has been modified for solving nonlinear initial value problems. The Laplace transform was used in this modification to eliminate the linear differential operator in the differential equation. The convergence of the solution was discussed according to the modification proposed. To illustrate this modification some examples were presented.

scholarly journals Formulation and Solution of th-Order Derivative Fuzzy Integrodifferential Equation Using New Iterative Method with a Reliable Algorithm

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
A. A. Hemeda
Keyword(s):  
Differential Equation ◽  
Approximate Solution ◽  
Differential Equations ◽  
Iterative Method ◽  
Integrodifferential Equation ◽  
Order Derivative ◽  
Parametric Form ◽  
Numerical Examples ◽  
Integro Differential Equation ◽  
New Iterative Method

Thenth-order derivative fuzzy integro-differential equation in parametric form is converted to its crisp form, and then the new iterative method with a reliable algorithm is used to obtain an approximate solution for this crisp form. The analysis is accompanied by numerical examples which confirm efficiency and power of this method in solving fuzzy integro-differential equations.

scholarly journals New Approaches to the General Linearization Problem of Jacobi Polynomials Based on Moments and Connection Formulas

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1573
Author(s):  
Waleed Mohamed Abd-Elhameed ◽  
Badah Mohamed Badah
Keyword(s):  
Differential Equation ◽  
Hypergeometric Functions ◽  
Jacobi Polynomials ◽  
Tau Method ◽  
Riccati Differential Equation ◽  
Shifted Jacobi Polynomials ◽  
Linearization Problem ◽  
Linearization Coefficients ◽  
New Formula ◽  
Connection Formulas

This article deals with the general linearization problem of Jacobi polynomials. We provide two approaches for finding closed analytical forms of the linearization coefficients of these polynomials. The first approach is built on establishing a new formula in which the moments of the shifted Jacobi polynomials are expressed in terms of other shifted Jacobi polynomials. The derived moments formula involves a hypergeometric function of the type 4F3(1), which cannot be summed in general, but for special choices of the involved parameters, it can be summed. The reduced moments formulas lead to establishing new linearization formulas of certain parameters of Jacobi polynomials. Another approach for obtaining other linearization formulas of some Jacobi polynomials depends on making use of the connection formulas between two different Jacobi polynomials. In the two suggested approaches, we utilize some standard reduction formulas for certain hypergeometric functions of the unit argument such as Watson’s and Chu-Vandermonde identities. Furthermore, some symbolic algebraic computations such as the algorithms of Zeilberger, Petkovsek and van Hoeij may be utilized for the same purpose. As an application of some of the derived linearization formulas, we propose a numerical algorithm to solve the non-linear Riccati differential equation based on the application of the spectral tau method.

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