Reformulated Adomian Decomposition Method for the Approximation of Special Linear and Nonlinear Two-Point Boundary Value Problems

2021 ◽  
Vol 21 (2) ◽  
pp. 410
Author(s):  
Joshua Sunday ◽  
Joshua Kwanamu ◽  
Nathaniel Kamoh ◽  
Yusuf Skwame
Keyword(s):  
Boundary Value Problems ◽  
Decomposition Method ◽  
Boundary Value ◽  
Adomian Decomposition Method ◽  
Point Boundary ◽  
Special Linear ◽  
Adomian Decomposition ◽  
Linear And Nonlinear

A Reliable Treatment for Solving Nonlinear Two-Point Boundary Value Problems

2007 ◽  
Vol 62 (9) ◽  
pp. 483-489
Author(s):  
Mustafa Inc
Keyword(s):  
Boundary Value Problems ◽  
Numerical Experiments ◽  
Decomposition Method ◽  
Shooting Method ◽  
Boundary Value ◽  
Adomian Decomposition Method ◽  
Point Boundary ◽  
Adomian Decomposition

In this paper, we study the modified decomposition method (MDM) for solving nonlinear twopoint boundary value problems (BVPs) and show numerical experiments. The modified form of the Adomian decomposition method which is more fast and accurate than the standard decomposition method (SDM) was introduced by Wazwaz. In addition, we will compare the performance of the MDM and the new nonlinear shooting method applied to the solutions of nonlinear two-point BVPs. The comparison shows that the MDM is reliable, efficient and easy for solving the nonlinear twopoint BVPs.

scholarly journals New Approach for Solving a Class of Doubly Singular Two-Point Boundary Value Problems Using Adomian Decomposition Method

2012 ◽  
Vol 2012 ◽  
pp. 1-22 ◽  
Author(s):  
Randhir Singh ◽  
Jitendra Kumar ◽  
Gnaneshwar Nelakanti
Keyword(s):  
Boundary Value Problems ◽  
Decomposition Method ◽  
Boundary Value ◽  
Adomian Decomposition Method ◽  
Multiple Roots ◽  
Point Boundary ◽  
New Approach ◽  
Successive Solution ◽  
Adomian Decomposition ◽  
Complete Calculation

We propose two new modified recursive schemes for solving a class of doubly singular two-point boundary value problems. These schemes are based on Adomian decomposition method (ADM) and new proposed integral operators. We use all the boundary conditions to derive an integral equation before establishing the recursive schemes for the solution components. Thus we develop recursive schemes without any undetermined coefficients while computing successive solution components, whereas several previous recursive schemes have done so. This modification also avoids solving a sequence of nonlinear algebraic or transcendental equations for the undetermined coefficients with multiple roots, which is required to complete calculation of the solution by several earlier modified recursion schemes using the ADM. The approximate solution is computed in the form of series with easily calculable components. The effectiveness of the proposed approach is tested by considering four examples and results are compared with previous known results.

scholarly journals Solving a Class of Singular Two-Point Boundary Value Problems Using New Modified Decomposition Method

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Randhir Singh ◽  
Jitendra Kumar
Keyword(s):  
Boundary Value Problems ◽  
Decomposition Method ◽  
Boundary Value ◽  
Adomian Decomposition Method ◽  
Point Boundary ◽  
Recursive Scheme ◽  
Successive Solution ◽  
Adomian Decomposition ◽  
Present Technique ◽  
Transcendental Equations

We introduce an effective methodology for solving a class of linear as well as nonlinear singular two-point boundary value problems. This methodology is based on a modification of Adomian decomposition method (ADM) and a new two fold integral operator. We use all the boundary conditions to derive an integral equation before establishing the recursive scheme for the solution components of solution. Thus, we develop modified recursive scheme without any undetermined coefficients while computing the successive solution components. This modification also avoids solving a sequence of nonlinear algebraic or transcendental equations for the undetermined coefficients. However, most of earlier recursive schemes using ADM do require computation of undetermined coefficients. The approximate solution is obtained in the form of series with easily calculable components. Numerical examples are included to demonstrate the accuracy, applicability, and generality of the present technique. The results reveal that the method is very effective, straightforward, and simple.

scholarly journals Solution of Two-Point Linear and Nonlinear Boundary Value Problems with Neumann Boundary Conditions Using a New Modified Adomian Decomposition Method

2020 ◽  
pp. 49-60
Author(s):  
Justina Mulenga ◽  
Patrick Azere Phiri
Keyword(s):  
Boundary Value Problems ◽  
Decomposition Method ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Adomian Decomposition Method ◽  
Nonlinear Boundary Value Problems ◽  
Modified Adomian Decomposition Method ◽  
Adomian Decomposition ◽  
Nonlinear Boundary Value ◽  
Linear And Nonlinear

In this paper, we present the New Modified Adomian Decomposition Method which is a modification of the Modified Adomian Decomposition Method. The new method incorporates the inverse linear operator theorem into the modified Adomian decomposition method for the calculation of u0. Six linear and nonlinear boundary value problems with Neumann conditions are solved in order to test the method. The results show that the method is effective.

Exact Solutions for a Class of Nonlinear Singular Two-Point Boundary Value Problems: The Decomposition Method

2010 ◽  
Vol 65 (3) ◽  
pp. 145-150 ◽  
Author(s):  
Abd Elhalim Ebaid
Keyword(s):  
Exact Solutions ◽  
Closed Form ◽  
Boundary Value Problems ◽  
Decomposition Method ◽  
Applied Mathematics ◽  
Boundary Value ◽  
Adomian Decomposition Method ◽  
Point Boundary ◽  
Adomian Decomposition ◽  
First Time

Many problems in applied mathematics and engineering are usually formulated as singular two-point boundary value problems. A well-known fact is that the exact solutions in closed form of such problems were not obtained in many cases. In this paper, the exact solutions for a class of nonlinear singular two-point boundary value problems are obtained to the first time by using Adomian decomposition method

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