By applying iterative technique,we obtain the existence of positive solutions for a singular Riemann-Stieltjes integral boundary value problem in the case that f（t,u） is non-increasing respect to u.
In this paper, we are concerned with the symmetric positive solutions of a 2n-order boundary value problems on time scales. By using induction principle,the symmetric form of the Green＇s function is established. In o...In this paper, we are concerned with the symmetric positive solutions of a 2n-order boundary value problems on time scales. By using induction principle,the symmetric form of the Green＇s function is established. In order to construct a necessary and sufficient condition for the existence result, the method of iterative technique will be used. As an application, an example is given to illustrate our main result.展开更多
In this paper,we have proposed a numerical method for Singularly Perturbed Boundary Value Problems(SPBVPs)of convection-diffusion type of third order Ordinary Differential Equations(ODEs)in which the SPBVP is reduced ...In this paper,we have proposed a numerical method for Singularly Perturbed Boundary Value Problems(SPBVPs)of convection-diffusion type of third order Ordinary Differential Equations(ODEs)in which the SPBVP is reduced into a weakly coupled system of two ODEs subject to suitable initial and boundary conditions.The numerical method combines boundary value technique,asymptotic expansion approximation,shooting method and finite difference scheme.In order to get a numerical solution for the derivative of the solution,the domain is divided into two regions namely inner region and outer region.The shooting method is applied to the inner region while standard finite difference scheme(FD)is applied for the outer region.Necessary error estimates are derived for the method.Computational efficiency and accuracy are verified through numerical examples.The method is easy to implement and suitable for parallel computing.展开更多
基金supported by Program for Scientific research innovation team in Colleges and universities of Shandong Provincethe Doctoral Program Foundation of Education Ministry of China(20133705110003)+1 种基金the Natural Science Foundation of Shandong Province of China(ZR2014AM007)the National Natural Science Foundation of China(11571197)
文摘By applying iterative technique,we obtain the existence of positive solutions for a singular Riemann-Stieltjes integral boundary value problem in the case that f（t,u） is non-increasing respect to u.
基金Supported by NNSF of China(11201213,11371183)NSF of Shandong Province(ZR2010AM022,ZR2013AM004)+2 种基金the Project of Shandong Provincial Higher Educational Science and Technology(J15LI07)the Project of Ludong University High-Quality Curriculum(20130345)the Teaching Reform Project of Ludong University in 2014(20140405)
文摘In this paper, we are concerned with the symmetric positive solutions of a 2n-order boundary value problems on time scales. By using induction principle,the symmetric form of the Green＇s function is established. In order to construct a necessary and sufficient condition for the existence result, the method of iterative technique will be used. As an application, an example is given to illustrate our main result.
文摘In this paper,we have proposed a numerical method for Singularly Perturbed Boundary Value Problems(SPBVPs)of convection-diffusion type of third order Ordinary Differential Equations(ODEs)in which the SPBVP is reduced into a weakly coupled system of two ODEs subject to suitable initial and boundary conditions.The numerical method combines boundary value technique,asymptotic expansion approximation,shooting method and finite difference scheme.In order to get a numerical solution for the derivative of the solution,the domain is divided into two regions namely inner region and outer region.The shooting method is applied to the inner region while standard finite difference scheme(FD)is applied for the outer region.Necessary error estimates are derived for the method.Computational efficiency and accuracy are verified through numerical examples.The method is easy to implement and suitable for parallel computing.
