scholarly journals On approximate solutions of initial value problems for integro-differential equation with quasilinear differential operator and generalized Volterra operator

1969 ◽  
Vol 094 (1) ◽  
pp. 21-33
Author(s):  
Vladimir Fedorovitch Krapivin
Keyword(s):  
Differential Equation ◽  
Differential Operator ◽  
Initial Value Problems ◽  
Volterra Operator ◽  
Approximate Solutions ◽  
Initial Value ◽  
Integro Differential Equation

scholarly journals Solving Ordinary Differential Equation of Higher Order by Adomian Decomposition Method

2020 ◽  
pp. 44-53
Author(s):  
Sumayah Ghaleb Othman ◽  
Yahya Qaid Hasan
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Initial Value Problems ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Approximate Solutions ◽  
Higher Order ◽  
Initial Value ◽  
Adomian Decomposition ◽  
Different Types

Aims/ Objectives: In this article, we use Adomian Decomposition method (ADM) for solving initial value problems in the higher order ordinary differential equations. Many researchers have used the ADM in order to find convergent as well as exact solutions of different types of equations. Therefore, the ADM is considered as an effective and successful method for solving differential equations. In this paper, we presented some suggested amendments to the ADM by using a new differential operator in order to find solutions for higher order types of equations. We demonstrated the effectiveness of this method through many examples and we find out that we get an approximate solutions using the proposed amendments. We can conclude that the suggested modification of ADM is afftective and produces reliable results.

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 Approximate solution of nonlinear ordinary differential equation using ZZ decomposition method

2020 ◽  
Vol 4 (1) ◽  
pp. 448-455
Author(s):  
Mulugeta Andualem ◽  
◽  
Atinafu Asfaw ◽  
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Approximate Solution ◽  
Initial Value Problems ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Nonlinear Ordinary Differential Equation ◽  
Initial Value ◽  
Transform Method ◽  
Adomian Decomposition

Nonlinear initial value problems are somewhat difficult to solve analytically as well as numerically related to linear initial value problems as their variety of natures. Because of this, so many scientists still searching for new methods to solve such nonlinear initial value problems. However there are many methods to solve it. In this article we have discussed about the approximate solution of nonlinear first order ordinary differential equation using ZZ decomposition method. This method is a combination of the natural transform method and Adomian decomposition method.

Solvability of initial value problems with fractional order differential equations in banach spaces by α-dense curves

2017 ◽  
Vol 20 (3) ◽  
Author(s):  
Gonzalo García
Keyword(s):  
Differential Equation ◽  
Banach Space ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Initial Value Problems ◽  
Existence Of Solutions ◽  
Initial Value ◽  
Measures Of Noncompactness ◽  
Fractional Order Differential Equations ◽  
Fractional Differential

AbstractIn this paper we study the existence of solutions for an initial value problem, posed in a given Banach space, with a fractional differential equation via densifiability techniques. For our goal, we will prove a new fixed point result (not based on measures of noncompactness) which is, in forms, a generalization of the well-known Darbo’s fixed point theorem but essentially different. Some illustrative examples are given.

scholarly journals Generalized quasilinearization method for nonlinear functional differential equations

2003 ◽  
Vol 16 (1) ◽  
pp. 33-43 ◽  
Author(s):  
Bashir Ahmad ◽  
Rehmat Ali Khan ◽  
S. Sivasundaram
Keyword(s):  
Differential Equations ◽  
Rate Of Convergence ◽  
Initial Value Problems ◽  
Functional Differential Equations ◽  
Approximate Solutions ◽  
Monotone Sequence ◽  
Quasilinearization Method ◽  
Initial Value ◽  
Nonlinear Functional ◽  
Functional Differential

We develop a generalized quasilinearization method for nonlinear initial value problems involving functional differential equations and obtain a sequence of approximate solutions converging monotonically and quadratically to the solution of the problem. In addition, we obtain a monotone sequence of approximate solutions converging uniformly to the solution of the problem, possessing the rate of convergence higher than quadratic.

scholarly journals A Numerical Method for Lane-Emden Equations Using Hybrid Functions and the Collocation Method

2012 ◽  
Vol 2012 ◽  
pp. 1-9 ◽  
Author(s):  
Changqing Yang ◽  
Jianhua Hou
Keyword(s):  
Differential Equation ◽  
Numerical Method ◽  
Collocation Method ◽  
Chebyshev Polynomials ◽  
Initial Value Problems ◽  
Algebraic Equations ◽  
Initial Value ◽  
Numerical Examples ◽  
Hybrid Functions ◽  
Block Pulse Functions

A numerical method to solve Lane-Emden equations as singular initial value problems is presented in this work. This method is based on the replacement of unknown functions through a truncated series of hybrid of block-pulse functions and Chebyshev polynomials. The collocation method transforms the differential equation into a system of algebraic equations. It also has application in a wide area of differential equations. Corresponding numerical examples are presented to demonstrate the accuracy of the proposed method.

scholarly journals An existence theorem for solutions of an integro-differential equation in Banach spaces

2012 ◽  
Vol 45 (4) ◽  
Author(s):  
Aldona Dutkiewicz
Keyword(s):  
Differential Equation ◽  
Existence Theorem ◽  
Banach Spaces ◽  
Initial Value Problem ◽  
Initial Value ◽  
Measures Of Noncompactness ◽  
Integro Differential Equation ◽  
Local Solutions

AbstractThe paper contains an existence theorem for local solutions of an initial value problem for a nonlinear integro-differential equation in Banach spaces. The assumptions and proofs are expressed in terms of measures of noncompactness.

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