SU\G(𝔸)/K·U
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Application of the Kamal-He’s Iterative Method to Klein-Gordons Equations

2025-04-07
Adejoh Jeremiah , M. Y. Adamu , A. G. Madaki +2 more
This study demonstrates the effectiveness and accuracy of the KHM for solving both linear and nonlinear Klein-Gordon equations. Through graphical comparisons with other methods such as VIM, TAM, and NIM, … This study demonstrates the effectiveness and accuracy of the KHM for solving both linear and nonlinear Klein-Gordon equations. Through graphical comparisons with other methods such as VIM, TAM, and NIM, and error analysis, the results confirm the high precision and reliability of KHM. The approach is shown to be straightforward, easy to implement, and highly efficient for solving linear PDEs. Additionally, KHM provides the exact solution for nonlinear Klein-Gordon equations in a single iteration, highlighting its computational efficiency. Overall, the KHM is proven to be a powerful and reliable tool for solving a wide range of equations in mathematical physics.

Enhancement of the Kamal Transform Method with the He’s Polynomial for Solving Partial Differential Equations (Telegraph Equation)

2025-04-08
Ogboche Abichele , I. B. Mshelia , A. G. Madaki +3 more
This study proposes a hybrid solution methodology that integrates the Kamal Transform Method (KTM) with He’s Polynomial Method (HPM) for solving nonlinear partial differential equations (PDEs), with a focus on … This study proposes a hybrid solution methodology that integrates the Kamal Transform Method (KTM) with He’s Polynomial Method (HPM) for solving nonlinear partial differential equations (PDEs), with a focus on the telegraph equation. The telegraph equation, which models wave propagation and diffusive behaviors, presents significant challenges in terms of nonlinearity, complex boundary conditions, and slow convergence in traditional methods. By combining the transformation power of the Kamal method with the iterative, rapidly converging He’s polynomial method, this research aims to enhance the accuracy, convergence, and computational efficiency of existing solution techniques for PDEs. The proposed hybrid approach is applied to both linear and nonlinear forms of the telegraph equation, demonstrating excellent agreement with exact solutions and offering significant improvements in accuracy, especially in the presence of nonlinearities. Comparative analyses with traditional methods, including Elzaki's transform, show that the Kamal-He’s polynomial method outperforms existing techniques in terms of error reduction. The results highlight the method's potential for broader application in various fields of engineering, physics, and applied sciences, where complex, nonlinear PDEs are commonly encountered.

A One-Step Modified New Iterative Method for Solving Partial Differential Equation

2025-04-28
I. Abdulmalik , A. M. Kwami , J. O. Okai +3 more
This study introduces a reliable semi-analytical approach for solving partial differential equations (PDEs) using a Modified New Iterative Method (MNIM). The primary aim is to enhance the efficiency of deriving … This study introduces a reliable semi-analytical approach for solving partial differential equations (PDEs) using a Modified New Iterative Method (MNIM). The primary aim is to enhance the efficiency of deriving closed-form solutions through an innovative formulation of an integral operator based on n-fold integration. This approach circumvents the conventional necessity of transforming PDEs into systems of multiple integral equations, thereby streamlining the solution process. The effectiveness of the MNIM is assessed through a series of examples, demonstrating its rapid convergence and superior performance in solving an array of evolution and partial differential equations. The results indicate that the MNIM not only simplifies the solution process but also significantly improves computational efficiency compared to traditional methods. This contribution holds substantial implications for both theoretical advancements in numerical analysis and practical applications across various fields where PDEs are prevalent, thereby facilitating more effective problem-solving strategies in complex systems.

Mathematical Model of Transmission Dynamic of Ebola Virus Disease

2025-04-30
Samuel Yohanna , M. Adamu , Hina Ahmed +2 more
This study investigates the impact of treatment and vaccination on the transmission dynamics of Ebola virus disease (EVD) within human populations, as well as the effects of environmental factors on … This study investigates the impact of treatment and vaccination on the transmission dynamics of Ebola virus disease (EVD) within human populations, as well as the effects of environmental factors on vector populations. We formulated a system of ordinary differential equations (ODEs) to model these dynamics and applied the method of linearized stability analysis to solve the equations. The stability analysis revealed that the disease-free equilibrium (DFE) states of the models remain stable when certain parameters—specifically, the treatment rate in the human population and the recovery rate in the vector population—are appropriately adjusted. Numerical simulations demonstrated that achieving a disease-free equilibrium state requires simultaneous treatment and vaccination of the population. The findings highlight the necessity of integrated intervention strategies to effectively control EVD transmission, contributing valuable insights for public health policy and future research on infectious disease management.

A Simplified Hybrid Analytical Method for Solving Integer and Fractional-Order Differential Equations without Adomian Polynomials or Lagrange Multipliers

2025-05-18
J. O. Okai , Michael Cornelius , I. Abdulmalik +4 more
In this study, we propose a novel hybrid analytical technique that combines the Adomian Decomposition Method (ADM) with the Variational Iteration Method (VIM) to solve a class of linear and … In this study, we propose a novel hybrid analytical technique that combines the Adomian Decomposition Method (ADM) with the Variational Iteration Method (VIM) to solve a class of linear and nonlinear first-order initial value problems (IVPs), including those of fractional order. The principal aim of this approach is to overcome the computational challenges typically encountered in each individual method—namely, the complexity of generating Adomian polynomials in ADM and the requirement for Lagrange multipliers in VIM. By synthesizing the strengths of both methods, the hybrid scheme constructs analytical series solutions without necessitating linearization, Adomian polynomials, or the explicit formulation of Lagrange multipliers. This significantly streamlines the solution process while preserving accuracy and generality. The validity and computational efficiency of the proposed method are substantiated through a series of illustrative examples, encompassing both integer-order and fractional differential equations. The results demonstrate that the hybrid approach not only simplifies implementation but also yields precise and rapidly converging solutions, making it a robust alternative for tackling a broad spectrum of initial value problems in mathematical modeling and applied sciences.

A Hybrid Approach of the Variational Iteration Method and Adomian Decomposition Method for Solving Fractional Integro-Differential Equations

2025-05-18
Okai J. O , M. Y. Adamu , Michael Cornelius +6 more
In this study, we propose a hybrid analytical technique that integrates the Adomian Decomposition Method (ADM) with the Variational Iteration Method (VIM) to solve both linear and nonlinear integro-differential equations … In this study, we propose a hybrid analytical technique that integrates the Adomian Decomposition Method (ADM) with the Variational Iteration Method (VIM) to solve both linear and nonlinear integro-differential equations of integer and fractional orders. This approach extends and refines the Odibat Decomposition Method (ODM) by addressing key limitations inherent in ADM and VIM—specifically, the reliance on linearization, Adomian polynomials, and Lagrange multipliers. By circumventing these computational complexities, the proposed method enables the direct and efficient construction of series solutions with improved convergence properties. The hybrid scheme is designed for broader applicability and enhanced computational simplicity, making it a powerful tool for analyzing complex integro-differential systems. Its effectiveness and robustness are demonstrated through a range of illustrative examples, confirming the method’s capability to provide accurate analytical approximations with minimal computational overhead.

A Simplified Hybrid Analytical Method for Solving Integer and Fractional-Order Differential Equations without Adomian Polynomials or Lagrange Multipliers

2025-05-18
J. O. Okai , Michael Cornelius , I. Abdulmalik +4 more
In this study, we propose a novel hybrid analytical technique that combines the Adomian Decomposition Method (ADM) with the Variational Iteration Method (VIM) to solve a class of linear and … In this study, we propose a novel hybrid analytical technique that combines the Adomian Decomposition Method (ADM) with the Variational Iteration Method (VIM) to solve a class of linear and nonlinear first-order initial value problems (IVPs), including those of fractional order. The principal aim of this approach is to overcome the computational challenges typically encountered in each individual method—namely, the complexity of generating Adomian polynomials in ADM and the requirement for Lagrange multipliers in VIM. By synthesizing the strengths of both methods, the hybrid scheme constructs analytical series solutions without necessitating linearization, Adomian polynomials, or the explicit formulation of Lagrange multipliers. This significantly streamlines the solution process while preserving accuracy and generality. The validity and computational efficiency of the proposed method are substantiated through a series of illustrative examples, encompassing both integer-order and fractional differential equations. The results demonstrate that the hybrid approach not only simplifies implementation but also yields precise and rapidly converging solutions, making it a robust alternative for tackling a broad spectrum of initial value problems in mathematical modeling and applied sciences.

A Hybrid Approach of the Variational Iteration Method and Adomian Decomposition Method for Solving Fractional Integro-Differential Equations

2025-05-18
Okai J. O , M. Y. Adamu , Michael Cornelius +6 more
In this study, we propose a hybrid analytical technique that integrates the Adomian Decomposition Method (ADM) with the Variational Iteration Method (VIM) to solve both linear and nonlinear integro-differential equations … In this study, we propose a hybrid analytical technique that integrates the Adomian Decomposition Method (ADM) with the Variational Iteration Method (VIM) to solve both linear and nonlinear integro-differential equations of integer and fractional orders. This approach extends and refines the Odibat Decomposition Method (ODM) by addressing key limitations inherent in ADM and VIM—specifically, the reliance on linearization, Adomian polynomials, and Lagrange multipliers. By circumventing these computational complexities, the proposed method enables the direct and efficient construction of series solutions with improved convergence properties. The hybrid scheme is designed for broader applicability and enhanced computational simplicity, making it a powerful tool for analyzing complex integro-differential systems. Its effectiveness and robustness are demonstrated through a range of illustrative examples, confirming the method’s capability to provide accurate analytical approximations with minimal computational overhead.

Mathematical Model of Transmission Dynamic of Ebola Virus Disease

2025-04-30
Samuel Yohanna , M. Adamu , Hina Ahmed +2 more
This study investigates the impact of treatment and vaccination on the transmission dynamics of Ebola virus disease (EVD) within human populations, as well as the effects of environmental factors on … This study investigates the impact of treatment and vaccination on the transmission dynamics of Ebola virus disease (EVD) within human populations, as well as the effects of environmental factors on vector populations. We formulated a system of ordinary differential equations (ODEs) to model these dynamics and applied the method of linearized stability analysis to solve the equations. The stability analysis revealed that the disease-free equilibrium (DFE) states of the models remain stable when certain parameters—specifically, the treatment rate in the human population and the recovery rate in the vector population—are appropriately adjusted. Numerical simulations demonstrated that achieving a disease-free equilibrium state requires simultaneous treatment and vaccination of the population. The findings highlight the necessity of integrated intervention strategies to effectively control EVD transmission, contributing valuable insights for public health policy and future research on infectious disease management.

A One-Step Modified New Iterative Method for Solving Partial Differential Equation

2025-04-28
I. Abdulmalik , A. M. Kwami , J. O. Okai +3 more
This study introduces a reliable semi-analytical approach for solving partial differential equations (PDEs) using a Modified New Iterative Method (MNIM). The primary aim is to enhance the efficiency of deriving … This study introduces a reliable semi-analytical approach for solving partial differential equations (PDEs) using a Modified New Iterative Method (MNIM). The primary aim is to enhance the efficiency of deriving closed-form solutions through an innovative formulation of an integral operator based on n-fold integration. This approach circumvents the conventional necessity of transforming PDEs into systems of multiple integral equations, thereby streamlining the solution process. The effectiveness of the MNIM is assessed through a series of examples, demonstrating its rapid convergence and superior performance in solving an array of evolution and partial differential equations. The results indicate that the MNIM not only simplifies the solution process but also significantly improves computational efficiency compared to traditional methods. This contribution holds substantial implications for both theoretical advancements in numerical analysis and practical applications across various fields where PDEs are prevalent, thereby facilitating more effective problem-solving strategies in complex systems.

Enhancement of the Kamal Transform Method with the He’s Polynomial for Solving Partial Differential Equations (Telegraph Equation)

2025-04-08
Ogboche Abichele , I. B. Mshelia , A. G. Madaki +3 more
This study proposes a hybrid solution methodology that integrates the Kamal Transform Method (KTM) with He’s Polynomial Method (HPM) for solving nonlinear partial differential equations (PDEs), with a focus on … This study proposes a hybrid solution methodology that integrates the Kamal Transform Method (KTM) with He’s Polynomial Method (HPM) for solving nonlinear partial differential equations (PDEs), with a focus on the telegraph equation. The telegraph equation, which models wave propagation and diffusive behaviors, presents significant challenges in terms of nonlinearity, complex boundary conditions, and slow convergence in traditional methods. By combining the transformation power of the Kamal method with the iterative, rapidly converging He’s polynomial method, this research aims to enhance the accuracy, convergence, and computational efficiency of existing solution techniques for PDEs. The proposed hybrid approach is applied to both linear and nonlinear forms of the telegraph equation, demonstrating excellent agreement with exact solutions and offering significant improvements in accuracy, especially in the presence of nonlinearities. Comparative analyses with traditional methods, including Elzaki's transform, show that the Kamal-He’s polynomial method outperforms existing techniques in terms of error reduction. The results highlight the method's potential for broader application in various fields of engineering, physics, and applied sciences, where complex, nonlinear PDEs are commonly encountered.

Application of the Kamal-He’s Iterative Method to Klein-Gordons Equations

2025-04-07
Adejoh Jeremiah , M. Y. Adamu , A. G. Madaki +2 more
This study demonstrates the effectiveness and accuracy of the KHM for solving both linear and nonlinear Klein-Gordon equations. Through graphical comparisons with other methods such as VIM, TAM, and NIM, … This study demonstrates the effectiveness and accuracy of the KHM for solving both linear and nonlinear Klein-Gordon equations. Through graphical comparisons with other methods such as VIM, TAM, and NIM, and error analysis, the results confirm the high precision and reliability of KHM. The approach is shown to be straightforward, easy to implement, and highly efficient for solving linear PDEs. Additionally, KHM provides the exact solution for nonlinear Klein-Gordon equations in a single iteration, highlighting its computational efficiency. Overall, the KHM is proven to be a powerful and reliable tool for solving a wide range of equations in mathematical physics.
Coauthor Papers Together
Ogboche Abichele 4
Okai J. O 4
I. Abdulmalik 3
J. O. Okai 2
A. G. Madaki 2
U. M. Nasir 2
Michael Cornelius 2
Michael Cornelius 2
Y. U. Hafsat 2
Hassan Araga 1
M. Y. Adamu 1
Aminu Barde 1
M. Adamu 1
Hina Ahmed 1
M. Y. Adamu 1
I. B. Mshelia 1
Samuel Yohanna 1
A. M. Kwami 1