scholarly journals A Metaheuristic Optimization Algorithm for Solving Higher-Order Boundary Value Problems

2022 ◽  
Vol 13 (1) ◽  
pp. 0-0
Keyword(s):  
Genetic Programming ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Higher Order ◽  
Programming Algorithm ◽  
Spline Collocation ◽  
Programming Technique ◽  
Transform Method ◽  
Differential Transform ◽  
Homotopy Analysis

An effective metaheuristic algorithm to solve the higher-order boundary value problems, called a genetic programming technique is presented. In this paper, a genetic programming algorithm, which depends on the syntax tree representation, is employed to obtain the analytical solutions of higher- order differential equations with the boundary conditions. The proposed algorithm can be produce an exact or approximate solution when the classical methods lead to unsatisfactory results. To illustrate the efficiency and accuracy of the designed algorithm, several examples are tested. Finally, the obtained results are compared with the existing methods such as the homotopy analysis method, the B-Spline collocation method and the differential transform method.

scholarly journals Differential Transform Technique for Higher Order Boundary Value Problems

2015 ◽  
Vol 9 (13) ◽  
pp. 224 ◽  
Author(s):  
Abiodun Adegboyega Opanuga ◽  
Hilary I. Okagbue ◽  
Sunday O. Edeki ◽  
Olasunmbo O. Agboola
Keyword(s):  
Exact Solution ◽  
Approximate Solution ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Higher Order ◽  
Differential Transform Method ◽  
Transform Method ◽  
Differential Transform

This paper presents the approximate solution of higher order boundary value problems by differential transform method. Two examples are considered to illustrate the efficiency of this method. The results converge rapidly to the exact solution and are shown in tables and graphs.

scholarly journals Numerical Solution of Higher Order Boundary Value Problems

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Shahid S. Siddiqi ◽  
Muzammal Iftikhar
Keyword(s):  
Boundary Value Problems ◽  
Homotopy Analysis Method ◽  
Present Method ◽  
Boundary Value ◽  
Approximate Solutions ◽  
Convergent Series ◽  
Higher Order ◽  
Analysis Method ◽  
Homotopy Analysis ◽  
Linear And Nonlinear

The aim of this paper is to use the homotopy analysis method (HAM), an approximating technique for solving linear and nonlinear higher order boundary value problems. Using HAM, approximate solutions of seventh-, eighth-, and tenth-order boundary value problems are developed. This approach provides the solution in terms of a convergent series. Approximate results are given for several examples to illustrate the implementation and accuracy of the method. The results obtained from this method are compared with the exact solutions and other methods (Akram and Rehman (2013), Farajeyan and Maleki (2012), Geng and Li (2009), Golbabai and Javidi (2007), He (2007), Inc and Evans (2004), Lamnii et al. (2008), Siddiqi and Akram (2007), Siddiqi et al. (2012), Siddiqi et al. (2009), Siddiqi and Iftikhar (2013), Siddiqi and Twizell (1996), Siddiqi and Twizell (1998), Torvattanabun and Koonprasert (2010), and Kasi Viswanadham and Raju (2012)) revealing that the present method is more accurate.

scholarly journals Numerical Treatment of Singularly Perturbed Two-Point Boundary Value Problems by Using Differential Transformation Method

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Nurettin Doğan ◽  
Vedat Suat Ertürk ◽  
Ömer Akın
Keyword(s):  
Boundary Value Problems ◽  
Present Method ◽  
Boundary Value ◽  
Transformation Method ◽  
High Accuracy ◽  
Singularly Perturbed ◽  
Point Boundary ◽  
Transform Method ◽  
Differential Transform ◽  
First Time

Differential transform method is adopted, for the first time, for solving linear singularly perturbed two-point boundary value problems. Four numerical examples are given to demonstrate the effectiveness of the present method. Results show that the numerical scheme is very effective and convenient for solving a large number of linear singularly perturbed two-point boundary value problems with high accuracy.

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