In this study,we investigate the seventh-order nonlinear Caputo time-fractional KdV equation.The suggested model's solutions,which have a series form,are obtained using the hybrid ZZ-transform under the aforementi...In this study,we investigate the seventh-order nonlinear Caputo time-fractional KdV equation.The suggested model's solutions,which have a series form,are obtained using the hybrid ZZ-transform under the aforementioned fractional operator.The proposed approach combines the homotopy perturbation method(HPM)and the ZZ-transform.We consider two specific examples with suitable initial conditions and find the series solution to test their applicability.To demonstrate the utility of the presented technique,we explore its applications to the fractional Sawada–Kotera–Ito problem and the Lax equation.We observe the impact of a few fractional orders on the wave solution evolution for the problems under consideration.We provide the efficiency and reliability of the ZZHPM by calculating the absolute error between the series solution and the exact solution of both the Sawada–Kotera–Ito and Lax equations.The convergence and uniqueness of the solution are portrayed via fixed-point theory.展开更多
The object of the paper is to establish an instability theorem for seventh-order differential equations of the form (1.10). The proof is based on the use of Krasovskii criteria.
In this paper, Adomian decomposition method (ADM) is implemented to approximate the solution of the Korteweg-de Vries (KdV) equations of seventh order, which are Kaup-Kuperschmidt equation and seventh order Kawahara e...In this paper, Adomian decomposition method (ADM) is implemented to approximate the solution of the Korteweg-de Vries (KdV) equations of seventh order, which are Kaup-Kuperschmidt equation and seventh order Kawahara equation. The results obtained by the ADM are compared with the exact solutions. It is found that the ADM is very efficient and convenient and can be applied to a large class of problems. The conservation properties of solution are examined by calculating the first three invariants.展开更多
In this article, we develop numerical method by constructing ninth degree spline function using extended cubic spline Bickley’s method to find the approximate solution of seventh order linear boundary value problems ...In this article, we develop numerical method by constructing ninth degree spline function using extended cubic spline Bickley’s method to find the approximate solution of seventh order linear boundary value problems at different step lengths. The approximate solution is compared with the solution obtained by eighth degree splines and exact solution. It has been observed that the approximate solution is an excellent agreement with exact solution. Low absolute error indicates that our numerical method is effective for solving high order linear boundary value problems.展开更多
We develop a numerical method for solving the boundary value problem of The Linear Seventh Ordinary Boundary Value Problem by using the seventh-degree B-Spline function. Formulation is based on particular terms of ord...We develop a numerical method for solving the boundary value problem of The Linear Seventh Ordinary Boundary Value Problem by using the seventh-degree B-Spline function. Formulation is based on particular terms of order of seventh order boundary value problem. We obtain Septic B-Spline formulation and the Collocation B-spline method is formulated as an approximation solution. We apply the presented method to solve an example of seventh order boundary value problem in which the result shows that there is an agreement between approximate solutions and exact solutions. Resulting in low absolute errors shows that the presented numerical method is effective for solving high order boundary value problems. Finally, a general conclusion has been included.展开更多
文摘In this study,we investigate the seventh-order nonlinear Caputo time-fractional KdV equation.The suggested model's solutions,which have a series form,are obtained using the hybrid ZZ-transform under the aforementioned fractional operator.The proposed approach combines the homotopy perturbation method(HPM)and the ZZ-transform.We consider two specific examples with suitable initial conditions and find the series solution to test their applicability.To demonstrate the utility of the presented technique,we explore its applications to the fractional Sawada–Kotera–Ito problem and the Lax equation.We observe the impact of a few fractional orders on the wave solution evolution for the problems under consideration.We provide the efficiency and reliability of the ZZHPM by calculating the absolute error between the series solution and the exact solution of both the Sawada–Kotera–Ito and Lax equations.The convergence and uniqueness of the solution are portrayed via fixed-point theory.
文摘The object of the paper is to establish an instability theorem for seventh-order differential equations of the form (1.10). The proof is based on the use of Krasovskii criteria.
文摘In this paper, Adomian decomposition method (ADM) is implemented to approximate the solution of the Korteweg-de Vries (KdV) equations of seventh order, which are Kaup-Kuperschmidt equation and seventh order Kawahara equation. The results obtained by the ADM are compared with the exact solutions. It is found that the ADM is very efficient and convenient and can be applied to a large class of problems. The conservation properties of solution are examined by calculating the first three invariants.
文摘In this article, we develop numerical method by constructing ninth degree spline function using extended cubic spline Bickley’s method to find the approximate solution of seventh order linear boundary value problems at different step lengths. The approximate solution is compared with the solution obtained by eighth degree splines and exact solution. It has been observed that the approximate solution is an excellent agreement with exact solution. Low absolute error indicates that our numerical method is effective for solving high order linear boundary value problems.
文摘We develop a numerical method for solving the boundary value problem of The Linear Seventh Ordinary Boundary Value Problem by using the seventh-degree B-Spline function. Formulation is based on particular terms of order of seventh order boundary value problem. We obtain Septic B-Spline formulation and the Collocation B-spline method is formulated as an approximation solution. We apply the presented method to solve an example of seventh order boundary value problem in which the result shows that there is an agreement between approximate solutions and exact solutions. Resulting in low absolute errors shows that the presented numerical method is effective for solving high order boundary value problems. Finally, a general conclusion has been included.
