This paper is concerned with the superconvergent points of the continuous Galerkin solutions for delay differential equations of pantograph type. We prove the local nodal superconvergence of continuous Galerkin soluti...This paper is concerned with the superconvergent points of the continuous Galerkin solutions for delay differential equations of pantograph type. We prove the local nodal superconvergence of continuous Galerkin solutions under uniform meshes and locate all the superconvergent points based on the supercloseness between the continuous Galerkin solution U and the interpolation Hhu of the exact solution u. The theoretical results are illustrated by numerical examples.展开更多
This paper is concerned with properties of exact solution of pantograph delay equation y ′′ (t)=ay ′ (t)+by(t)+cy(qt), 0<q<1. Firstly, the existence and uniqueness of the exact solution of equations are ...This paper is concerned with properties of exact solution of pantograph delay equation y ′′ (t)=ay ′ (t)+by(t)+cy(qt), 0<q<1. Firstly, the existence and uniqueness of the exact solution of equations are proved, and then the condition is investigated which guarantee the exact solution is asymptotic stable.展开更多
In this paper, the Adomian Decomposition Method (ADM) and the Differential Transform Method (DTM) are applied to solve the multi-pantograph delay equations. The sufficient conditions are given to assure the convergenc...In this paper, the Adomian Decomposition Method (ADM) and the Differential Transform Method (DTM) are applied to solve the multi-pantograph delay equations. The sufficient conditions are given to assure the convergence of these methods. Several examples are presented to demonstrate the efficiency and reliability of the ADM and the DTM;numerical results are discussed, compared with exact solution. The results of the ADM and the DTM show its better performance than others. These methods give the desired accurate results only in a few terms and in a series form of the solution. The approach is simple and effective. These methods are used to solve many linear and nonlinear problems and reduce the size of computational work.展开更多
基金the Research and Innovation Fund Project for College Student of Zhoukou Normal University"Synchronization of complex networks under aperiodic intermittent control strategy"(ZKNUD2021004)the Basic Research Plan of Key Scientific Research Projects for College and University in Henan Province"Soliton equation solution and its application"(18B110022)。
基金Acknowledgments. The second author is supported by NSFC （Nos. 11571027, 91430215）, by Beijing Nova Program （No. 2151100003150140） and by the Importation and Development of High-Caliber Talents Project of Beijing Municipal Institutions （No. CIT＆TCD201504012）. The third author is supported by the Natural Science Foundation of Fujian Province of China （No.2013J05015）, by NSFC （No.11301437）, and by the Fundamental Research ~nds for the Central Universities （No. 20720150004）.
文摘This paper is concerned with the superconvergent points of the continuous Galerkin solutions for delay differential equations of pantograph type. We prove the local nodal superconvergence of continuous Galerkin solutions under uniform meshes and locate all the superconvergent points based on the supercloseness between the continuous Galerkin solution U and the interpolation Hhu of the exact solution u. The theoretical results are illustrated by numerical examples.
文摘This paper is concerned with properties of exact solution of pantograph delay equation y ′′ (t)=ay ′ (t)+by(t)+cy(qt), 0<q<1. Firstly, the existence and uniqueness of the exact solution of equations are proved, and then the condition is investigated which guarantee the exact solution is asymptotic stable.
文摘In this paper, the Adomian Decomposition Method (ADM) and the Differential Transform Method (DTM) are applied to solve the multi-pantograph delay equations. The sufficient conditions are given to assure the convergence of these methods. Several examples are presented to demonstrate the efficiency and reliability of the ADM and the DTM;numerical results are discussed, compared with exact solution. The results of the ADM and the DTM show its better performance than others. These methods give the desired accurate results only in a few terms and in a series form of the solution. The approach is simple and effective. These methods are used to solve many linear and nonlinear problems and reduce the size of computational work.
