The Eulerian？Lagrangian method（ELM） has been used by many ocean models as the solution of the advection equation,but the numerical error caused by interpolation imposes restriction on its accuracy.In the present st...The Eulerian？Lagrangian method（ELM） has been used by many ocean models as the solution of the advection equation,but the numerical error caused by interpolation imposes restriction on its accuracy.In the present study,hybrid N-order Lagrangian interpolation ELM（Li ELM） is put forward in which the N-order Lagrangian interpolation is used at first,then the lower order Lagrangian interpolation is applied in the points where the interpolation results are abnormally higher or lower.The calculation results of a step-shaped salinity advection model are analyzed,which show that higher order（N=3？8） Li ELM can reduce the mean numerical error of salinity calculation,but the numerical oscillation error is still significant.Even number order Li ELM makes larger numerical oscillation error than its adjacent odd number order Li ELM.Hybrid N-order Li ELM can remove numerical oscillation,and it significantly reduces the mean numerical error when N is even and the current is in fixed direction,while it makes less effect on mean numerical error when N is odd or the current direction changes periodically.Hybrid odd number order Li ELM makes less mean numerical error than its adjacent even number order Li ELM when the current is in the fixed direction,while the mean numerical error decreases as N increases when the current direction changes periodically,so odd number of N may be better for application.Among various types of Hybrid N-order Li ELM,the scheme reducing N-order directly to 1st-order may be the optimal for synthetic selection of accuracy and computational efficiency.展开更多
This paper concerns N-order fixed point theory in partially ordered metric spaces. For the sake of simplicity, we start our investigations with the tripled case. We define tripled generalized Meir-Keeler type contract...This paper concerns N-order fixed point theory in partially ordered metric spaces. For the sake of simplicity, we start our investigations with the tripled case. We define tripled generalized Meir-Keeler type contraction which extends the definition of [Bessem Samet, Coupled fixed point theorems for a generalized Meir-Keeler contraction in partially ordered metric spaces, Nonlinear Anal. 72 (2010), 4508-4517]. We then discuss the existence and uniqueness of tripled fixed point theorems in partially ordered metric spaces. For general cases, we generalized our results to the N-order case. The results will promote the study of N-order fixed point theory.展开更多
In this paper, we propose a new perspective to discuss the N-order fixed point theory of set-valued and single-valued mappings. There are two aspects in our work: we first define a product metric space with a graph fo...In this paper, we propose a new perspective to discuss the N-order fixed point theory of set-valued and single-valued mappings. There are two aspects in our work: we first define a product metric space with a graph for the single-valued mapping whose conversion makes the results and proofs concise and straightforward, and then we propose an <em>SG</em>-contraction definition for set-valued mapping which is more general than some recent contraction’s definition. The results obtained in this paper extend and unify some recent results of other authors. Our method to discuss the N-order fixed point unifies <em>N</em>-order fixed point theory of set-valued and single-valued mappings.展开更多
基金financially supported by the National Natural Science Foundation of China(Grant Nos.40906044 and 41076048)the Fundamental Research Funds for the Central Universities Project(Grant No.2011B05714)
文摘The Eulerian？Lagrangian method（ELM） has been used by many ocean models as the solution of the advection equation,but the numerical error caused by interpolation imposes restriction on its accuracy.In the present study,hybrid N-order Lagrangian interpolation ELM（Li ELM） is put forward in which the N-order Lagrangian interpolation is used at first,then the lower order Lagrangian interpolation is applied in the points where the interpolation results are abnormally higher or lower.The calculation results of a step-shaped salinity advection model are analyzed,which show that higher order（N=3？8） Li ELM can reduce the mean numerical error of salinity calculation,but the numerical oscillation error is still significant.Even number order Li ELM makes larger numerical oscillation error than its adjacent odd number order Li ELM.Hybrid N-order Li ELM can remove numerical oscillation,and it significantly reduces the mean numerical error when N is even and the current is in fixed direction,while it makes less effect on mean numerical error when N is odd or the current direction changes periodically.Hybrid odd number order Li ELM makes less mean numerical error than its adjacent even number order Li ELM when the current is in the fixed direction,while the mean numerical error decreases as N increases when the current direction changes periodically,so odd number of N may be better for application.Among various types of Hybrid N-order Li ELM,the scheme reducing N-order directly to 1st-order may be the optimal for synthetic selection of accuracy and computational efficiency.
文摘This paper concerns N-order fixed point theory in partially ordered metric spaces. For the sake of simplicity, we start our investigations with the tripled case. We define tripled generalized Meir-Keeler type contraction which extends the definition of [Bessem Samet, Coupled fixed point theorems for a generalized Meir-Keeler contraction in partially ordered metric spaces, Nonlinear Anal. 72 (2010), 4508-4517]. We then discuss the existence and uniqueness of tripled fixed point theorems in partially ordered metric spaces. For general cases, we generalized our results to the N-order case. The results will promote the study of N-order fixed point theory.
文摘In this paper, we propose a new perspective to discuss the N-order fixed point theory of set-valued and single-valued mappings. There are two aspects in our work: we first define a product metric space with a graph for the single-valued mapping whose conversion makes the results and proofs concise and straightforward, and then we propose an <em>SG</em>-contraction definition for set-valued mapping which is more general than some recent contraction’s definition. The results obtained in this paper extend and unify some recent results of other authors. Our method to discuss the N-order fixed point unifies <em>N</em>-order fixed point theory of set-valued and single-valued mappings.
