Waleed Mohammed Al-Hayani - Academia.edu (original) (raw)
Papers by Waleed Mohammed Al-Hayani
Applied mathematics, 2014
In this paper, the Adomian decomposition method with Green's function (Standard Adomian and Modif... more In this paper, the Adomian decomposition method with Green's function (Standard Adomian and Modified Technique) is applied to solve linear and nonlinear tenth-order boundary value problems with boundary conditions defined at any order derivatives. The numerical results obtained with a small amount of computation are compared with the exact solutions to show the efficiency of the method. The results show that the decomposition method is of high accuracy, more convenient and efficient for solving high-order boundary value problems.
Applied Mathematics, 2019
In this paper, the standard homotopy analysis method was applied to initial value problems of the... more In this paper, the standard homotopy analysis method was applied to initial value problems of the second order with some types of discontinuities, for both linear and nonlinear cases. To show the high accuracy of the solution results compared with the exact solution, a comparison of the numerical results was made applying the standard homotopy analysis method with the iteration of the integral equation and the numerical solution with the Simpson rule. Also, the maximum absolute error, 2 ⋅ , the maximum relative error, the maximum residual error and the estimated order of convergence were given. The research is meaningful and I recommend it to be published in the journal.
Applied Mathematics, 2017
In this paper, Daftardar-Gejji and Jafari method is applied to solve fractional heat-like and wav... more In this paper, Daftardar-Gejji and Jafari method is applied to solve fractional heat-like and wave-like models with variable coefficients. The method is proved for a variety of problems in one, two and three dimensional spaces where analytical approximate solutions are obtained. The examples are presented to show the efficiency and simplicity of this method.
Iraqi journal of science, Jul 30, 2023
In this paper, the Adomian decomposition method (ADM) is successfully applied to find the approxi... more In this paper, the Adomian decomposition method (ADM) is successfully applied to find the approximate solutions for the system of fuzzy Fredholm integral equations (SFFIEs) and we also study the convergence of the technique. A consistent way to reduce the size of the computation is given to reach the exact solution. One of the best methods adopted to determine the behavior of the approximate solutions. Finally, the problems that have been addressed confirm the validity of the method applied in this research using a comparison by combining numerical methods such as the Trapezoidal rule and Simpson rule with ADM.
European Journal of Pure and Applied Mathematics, Jul 30, 2023
To obtain approximate-exact solutions to nonlocal initial-boundary value problems (IBVPs) of line... more To obtain approximate-exact solutions to nonlocal initial-boundary value problems (IBVPs) of linear and nonlinear parabolic and hyperbolic partial differential equations (PDEs) subject to initial and nonlocal boundary conditions of integral type, the homotopy perturbation method (HPM) is utilized in this study. The HPM is used to solve the specified nonlocal IBVPs, which are then transformed into local Dirichlet IBVPs. Some examples demonstrate how accurate and efficient the HPM.
Journal of Al-Qadisiyah for Computer Science and Mathematics
In this paper, we propose a technique called Homotopy Analysis Method (HAM) for solving linear sy... more In this paper, we propose a technique called Homotopy Analysis Method (HAM) for solving linear systems of Fredholm integral equations to find relatively close solutions. The HAM approach involves an auxiliary parameter that offers a straightforward method for adjusting and managing the region where the series of solutions converge. We demonstrate the effectiveness of the HAM approach through our experimental results. Additionally, we improve the HAM approach by incorporating a genetic algorithm (HAM-GA) to further optimize the solutions. The performance of HAM-GA is evaluated by comparing its results to those obtained by HAM, using the residual error function as a fitness function for the genetic algorithm.
European Journal of Pure and Applied Mathematics
In this research, we successfully demonstrated the use of the homotopy perturbation method with G... more In this research, we successfully demonstrated the use of the homotopy perturbation method with Green's function to find approximate solutions for the fuzzy system of boundary value problems. Our results showcase the effectiveness of this method in providing accurate and reliable solutions. Our results showcase the effectiveness of this method in providing accurate and reliable solutions. The consistent way to reduce the size of the computation gives to reach the exact solution is one of the best methods adopted to determine the behavior of the solution directly in order to determine the approximate solution analytically, Finally, the problems that have been addressed confirmed the validity of the method applied analytically in this research using comparison with some numerical problems
European Journal of Pure and Applied Mathematics
This paper presents the application of the Homotopy Analysis Method (HAM) for solving nonlinear s... more This paper presents the application of the Homotopy Analysis Method (HAM) for solving nonlinear system of Volterra integral equations used to obtain a reasonably approximate solution. The HAM contains the auxiliary parameter h which provides a simple way to adjust and control the convergence region of the solution series. The results show that the HAM is a very effective method as well. The results were compared with the solutions obtained by developing a homotopy analysis method using the genetic algorithm (HAM-GA), considering the residual error function as a fitness function of the genetic algorithm.
1ST SAMARRA INTERNATIONAL CONFERENCE FOR PURE AND APPLIED SCIENCES (SICPS2021): SICPS2021
This paper is used to solve the systems of linear Volterra integral equations by means of the com... more This paper is used to solve the systems of linear Volterra integral equations by means of the combined sumudu transform with Adomian decomposition process. We equate the numerical results with the exact solutions to demonstrate the high accuracy of the solution results. The results show that the approach is very straightforward and effective.
Feature extraction and classification of the histopathological image plays a significant role in ... more Feature extraction and classification of the histopathological image plays a significant role in prediction and diagnosis of diseases, such as breast cancer. The common issues of the features matrix are that many of features may not be relevant to their diseases. Feature selection has been proved to be an effective way to improve the result of many classification methods. In this paper, an adaptive sparse support vector is proposed, with the aim of identification features, by combining the support vector machine with the weighted L1-norm. Experimental results based on a publicly recent breast cancer histopathological image datasets show that the proposed method significantly outperforms three competitor methods in terms of overall classification accuracy and the number of selected Classification of Breast Cancer Histopathology Images…. features. Thus, the proposed method can be useful for medical image classification in the real clinical practice. Mathematics Subject Classification:...
Numerical Algorithms, 2005
... value problems Waleed Al-Hayani ∗ and Luis Casasús Departamento de Matemática Aplicada, Escue... more ... value problems Waleed Al-Hayani ∗ and Luis Casasús Departamento de Matemática Aplicada, Escuela Técnica Superior de Ingenieros Industriales, Universidad Politécnica de Madrid, C/José Gutiérrez Abascal, 2, 28006 Madrid, Spain E-mail: lcasasus@etsii.upm.es ...
Applied Mathematics Letters, 2006
In this paper we extend our results of L. Casasús, W. Al-Hayani [The decomposition method for ord... more In this paper we extend our results of L. Casasús, W. Al-Hayani [The decomposition method for ordinary differential equations with discontinuities, Appl. Math. Comput. 131 (2002) 245-251] to initial value problems with several types of discontinuities, giving relevant examples of linear and nonlinear cases.
Applied Mathematics and Computation, 2005
In this paper, the decomposition method is applied to initial value problems for systems of ordin... more In this paper, the decomposition method is applied to initial value problems for systems of ordinary differential equations in both linear and nonlinear cases, focusing our interest in stiff problems.
Applied Mathematics and Computation, 2002
In this paper, the decomposition method is applied to the Initial Value Problem (IVP) for ordinar... more In this paper, the decomposition method is applied to the Initial Value Problem (IVP) for ordinary differential equations with discontinuities for both linear and nonlinear cases.
Applied Mathematics, 2017
In this paper, Homotopy Analysis method with Genetic Algorithm is presented and used to obtain an... more In this paper, Homotopy Analysis method with Genetic Algorithm is presented and used to obtain an analytical solution for the time-dependent Emden-Fowler type of equations and wave-type equation with singular behavior at x = 0. The advantage of this single global method employed to present a reliable framework is utilized to overcome the singularity behavior at the point x = 0 for both models. The method is demonstrated for a variety of problems in one and higher dimensional spaces where approximate-exact solutions are obtained. The results obtained in all cases show the reliability and the efficiency of this method.
AL-Rafidain Journal of Computer Sciences and Mathematics
In this work, the homotopy perturbation method (HPM) is used to solve initial value problems of f... more In this work, the homotopy perturbation method (HPM) is used to solve initial value problems of first order with various types of discontinuities. The numerical results obtained (are compared) using the traditional HPM, and the integral equation of the nth equation with the solution numerical obtained using Simpson and Trapezoidal Rules to demonstrate that the solution results are extremely accurate when compared to the exact solution. The maximum absolute error, ‖ ‖ , maximum relative error, maximum residual error, and expected convergence order are also provided.
PROCEEDING OF THE 1ST INTERNATIONAL CONFERENCE ON ADVANCED RESEARCH IN PURE AND APPLIED SCIENCE (ICARPAS2021): Third Annual Conference of Al-Muthanna University/College of Science
This paper is used to solve the systems of linear Fredholm-Volterra integro-differential equation... more This paper is used to solve the systems of linear Fredholm-Volterra integro-differential equations (SLFVIDEs) and systems of linear Fredholm-Volterra integral equations (SLFVIEs) by means of the combined sumudu transform with Adomian decomposition process. The approximate solution obtained by CST-ADM has been improved by using the Padé approximation (PA) of order[p/q], Trapezoidal rule and Simpson rule. These proposed methods gave excellent results close to the exact solution. By use a comparison of the numerical results with the exact solutions to demonstrate the high accuracy of the solution results. The results show that the present method is very straightforward and effective.
Applied Mathematics & Information Sciences, 2016
In this paper, the combined Laplace transform-homotopy perturbation method C(LT-HPM) is presented... more In this paper, the combined Laplace transform-homotopy perturbation method C(LT-HPM) is presented and used to solve the initial value problem for the sine-Gordon equation to obtain the approximate-exact solutions. The results obtained show the reliability and the efficiency of this method.
Journal of Computational and Applied Mathematics, 2005
In this paper, the decomposition method is applied to boundary-value problems of ordinary differe... more In this paper, the decomposition method is applied to boundary-value problems of ordinary differential equations with a parameter exhibiting turning points.
European Journal of Pure and Applied Mathematics, 2022
In this paper, the Adomian decomposition method and Modified Technique are successfully applied t... more In this paper, the Adomian decomposition method and Modified Technique are successfully applied to find the approximate solutions of the fuzzy system of Volterra integro-differential equations. The approximate solutions obtained have been improved by using the iteration of the integral equation and the numerical solution with the Simpson rule and Trapezoidal rule. These proposed methods gave excellent results close to the exact solution. The results show that the present method is very straightforward and effective.
Applied mathematics, 2014
In this paper, the Adomian decomposition method with Green's function (Standard Adomian and Modif... more In this paper, the Adomian decomposition method with Green's function (Standard Adomian and Modified Technique) is applied to solve linear and nonlinear tenth-order boundary value problems with boundary conditions defined at any order derivatives. The numerical results obtained with a small amount of computation are compared with the exact solutions to show the efficiency of the method. The results show that the decomposition method is of high accuracy, more convenient and efficient for solving high-order boundary value problems.
Applied Mathematics, 2019
In this paper, the standard homotopy analysis method was applied to initial value problems of the... more In this paper, the standard homotopy analysis method was applied to initial value problems of the second order with some types of discontinuities, for both linear and nonlinear cases. To show the high accuracy of the solution results compared with the exact solution, a comparison of the numerical results was made applying the standard homotopy analysis method with the iteration of the integral equation and the numerical solution with the Simpson rule. Also, the maximum absolute error, 2 ⋅ , the maximum relative error, the maximum residual error and the estimated order of convergence were given. The research is meaningful and I recommend it to be published in the journal.
Applied Mathematics, 2017
In this paper, Daftardar-Gejji and Jafari method is applied to solve fractional heat-like and wav... more In this paper, Daftardar-Gejji and Jafari method is applied to solve fractional heat-like and wave-like models with variable coefficients. The method is proved for a variety of problems in one, two and three dimensional spaces where analytical approximate solutions are obtained. The examples are presented to show the efficiency and simplicity of this method.
Iraqi journal of science, Jul 30, 2023
In this paper, the Adomian decomposition method (ADM) is successfully applied to find the approxi... more In this paper, the Adomian decomposition method (ADM) is successfully applied to find the approximate solutions for the system of fuzzy Fredholm integral equations (SFFIEs) and we also study the convergence of the technique. A consistent way to reduce the size of the computation is given to reach the exact solution. One of the best methods adopted to determine the behavior of the approximate solutions. Finally, the problems that have been addressed confirm the validity of the method applied in this research using a comparison by combining numerical methods such as the Trapezoidal rule and Simpson rule with ADM.
European Journal of Pure and Applied Mathematics, Jul 30, 2023
To obtain approximate-exact solutions to nonlocal initial-boundary value problems (IBVPs) of line... more To obtain approximate-exact solutions to nonlocal initial-boundary value problems (IBVPs) of linear and nonlinear parabolic and hyperbolic partial differential equations (PDEs) subject to initial and nonlocal boundary conditions of integral type, the homotopy perturbation method (HPM) is utilized in this study. The HPM is used to solve the specified nonlocal IBVPs, which are then transformed into local Dirichlet IBVPs. Some examples demonstrate how accurate and efficient the HPM.
Journal of Al-Qadisiyah for Computer Science and Mathematics
In this paper, we propose a technique called Homotopy Analysis Method (HAM) for solving linear sy... more In this paper, we propose a technique called Homotopy Analysis Method (HAM) for solving linear systems of Fredholm integral equations to find relatively close solutions. The HAM approach involves an auxiliary parameter that offers a straightforward method for adjusting and managing the region where the series of solutions converge. We demonstrate the effectiveness of the HAM approach through our experimental results. Additionally, we improve the HAM approach by incorporating a genetic algorithm (HAM-GA) to further optimize the solutions. The performance of HAM-GA is evaluated by comparing its results to those obtained by HAM, using the residual error function as a fitness function for the genetic algorithm.
European Journal of Pure and Applied Mathematics
In this research, we successfully demonstrated the use of the homotopy perturbation method with G... more In this research, we successfully demonstrated the use of the homotopy perturbation method with Green's function to find approximate solutions for the fuzzy system of boundary value problems. Our results showcase the effectiveness of this method in providing accurate and reliable solutions. Our results showcase the effectiveness of this method in providing accurate and reliable solutions. The consistent way to reduce the size of the computation gives to reach the exact solution is one of the best methods adopted to determine the behavior of the solution directly in order to determine the approximate solution analytically, Finally, the problems that have been addressed confirmed the validity of the method applied analytically in this research using comparison with some numerical problems
European Journal of Pure and Applied Mathematics
This paper presents the application of the Homotopy Analysis Method (HAM) for solving nonlinear s... more This paper presents the application of the Homotopy Analysis Method (HAM) for solving nonlinear system of Volterra integral equations used to obtain a reasonably approximate solution. The HAM contains the auxiliary parameter h which provides a simple way to adjust and control the convergence region of the solution series. The results show that the HAM is a very effective method as well. The results were compared with the solutions obtained by developing a homotopy analysis method using the genetic algorithm (HAM-GA), considering the residual error function as a fitness function of the genetic algorithm.
1ST SAMARRA INTERNATIONAL CONFERENCE FOR PURE AND APPLIED SCIENCES (SICPS2021): SICPS2021
This paper is used to solve the systems of linear Volterra integral equations by means of the com... more This paper is used to solve the systems of linear Volterra integral equations by means of the combined sumudu transform with Adomian decomposition process. We equate the numerical results with the exact solutions to demonstrate the high accuracy of the solution results. The results show that the approach is very straightforward and effective.
Feature extraction and classification of the histopathological image plays a significant role in ... more Feature extraction and classification of the histopathological image plays a significant role in prediction and diagnosis of diseases, such as breast cancer. The common issues of the features matrix are that many of features may not be relevant to their diseases. Feature selection has been proved to be an effective way to improve the result of many classification methods. In this paper, an adaptive sparse support vector is proposed, with the aim of identification features, by combining the support vector machine with the weighted L1-norm. Experimental results based on a publicly recent breast cancer histopathological image datasets show that the proposed method significantly outperforms three competitor methods in terms of overall classification accuracy and the number of selected Classification of Breast Cancer Histopathology Images…. features. Thus, the proposed method can be useful for medical image classification in the real clinical practice. Mathematics Subject Classification:...
Numerical Algorithms, 2005
... value problems Waleed Al-Hayani ∗ and Luis Casasús Departamento de Matemática Aplicada, Escue... more ... value problems Waleed Al-Hayani ∗ and Luis Casasús Departamento de Matemática Aplicada, Escuela Técnica Superior de Ingenieros Industriales, Universidad Politécnica de Madrid, C/José Gutiérrez Abascal, 2, 28006 Madrid, Spain E-mail: lcasasus@etsii.upm.es ...
Applied Mathematics Letters, 2006
In this paper we extend our results of L. Casasús, W. Al-Hayani [The decomposition method for ord... more In this paper we extend our results of L. Casasús, W. Al-Hayani [The decomposition method for ordinary differential equations with discontinuities, Appl. Math. Comput. 131 (2002) 245-251] to initial value problems with several types of discontinuities, giving relevant examples of linear and nonlinear cases.
Applied Mathematics and Computation, 2005
In this paper, the decomposition method is applied to initial value problems for systems of ordin... more In this paper, the decomposition method is applied to initial value problems for systems of ordinary differential equations in both linear and nonlinear cases, focusing our interest in stiff problems.
Applied Mathematics and Computation, 2002
In this paper, the decomposition method is applied to the Initial Value Problem (IVP) for ordinar... more In this paper, the decomposition method is applied to the Initial Value Problem (IVP) for ordinary differential equations with discontinuities for both linear and nonlinear cases.
Applied Mathematics, 2017
In this paper, Homotopy Analysis method with Genetic Algorithm is presented and used to obtain an... more In this paper, Homotopy Analysis method with Genetic Algorithm is presented and used to obtain an analytical solution for the time-dependent Emden-Fowler type of equations and wave-type equation with singular behavior at x = 0. The advantage of this single global method employed to present a reliable framework is utilized to overcome the singularity behavior at the point x = 0 for both models. The method is demonstrated for a variety of problems in one and higher dimensional spaces where approximate-exact solutions are obtained. The results obtained in all cases show the reliability and the efficiency of this method.
AL-Rafidain Journal of Computer Sciences and Mathematics
In this work, the homotopy perturbation method (HPM) is used to solve initial value problems of f... more In this work, the homotopy perturbation method (HPM) is used to solve initial value problems of first order with various types of discontinuities. The numerical results obtained (are compared) using the traditional HPM, and the integral equation of the nth equation with the solution numerical obtained using Simpson and Trapezoidal Rules to demonstrate that the solution results are extremely accurate when compared to the exact solution. The maximum absolute error, ‖ ‖ , maximum relative error, maximum residual error, and expected convergence order are also provided.
PROCEEDING OF THE 1ST INTERNATIONAL CONFERENCE ON ADVANCED RESEARCH IN PURE AND APPLIED SCIENCE (ICARPAS2021): Third Annual Conference of Al-Muthanna University/College of Science
This paper is used to solve the systems of linear Fredholm-Volterra integro-differential equation... more This paper is used to solve the systems of linear Fredholm-Volterra integro-differential equations (SLFVIDEs) and systems of linear Fredholm-Volterra integral equations (SLFVIEs) by means of the combined sumudu transform with Adomian decomposition process. The approximate solution obtained by CST-ADM has been improved by using the Padé approximation (PA) of order[p/q], Trapezoidal rule and Simpson rule. These proposed methods gave excellent results close to the exact solution. By use a comparison of the numerical results with the exact solutions to demonstrate the high accuracy of the solution results. The results show that the present method is very straightforward and effective.
Applied Mathematics & Information Sciences, 2016
In this paper, the combined Laplace transform-homotopy perturbation method C(LT-HPM) is presented... more In this paper, the combined Laplace transform-homotopy perturbation method C(LT-HPM) is presented and used to solve the initial value problem for the sine-Gordon equation to obtain the approximate-exact solutions. The results obtained show the reliability and the efficiency of this method.
Journal of Computational and Applied Mathematics, 2005
In this paper, the decomposition method is applied to boundary-value problems of ordinary differe... more In this paper, the decomposition method is applied to boundary-value problems of ordinary differential equations with a parameter exhibiting turning points.
European Journal of Pure and Applied Mathematics, 2022
In this paper, the Adomian decomposition method and Modified Technique are successfully applied t... more In this paper, the Adomian decomposition method and Modified Technique are successfully applied to find the approximate solutions of the fuzzy system of Volterra integro-differential equations. The approximate solutions obtained have been improved by using the iteration of the integral equation and the numerical solution with the Simpson rule and Trapezoidal rule. These proposed methods gave excellent results close to the exact solution. The results show that the present method is very straightforward and effective.