A numerical approach is an effective means of solving boundary value problems(BVPs).This study focuses on physical problems with general partial differential equations(PDEs).It investigates the solution approach throu...A numerical approach is an effective means of solving boundary value problems(BVPs).This study focuses on physical problems with general partial differential equations(PDEs).It investigates the solution approach through the standard forms of the PDE module in COMSOL.Two typical mechanics problems are exemplified:The deflection of a thin plate,which can be addressed with the dedicated finite element module,and the stress of a pure bending beamthat cannot be tackled.The procedure for the two problems regarding the three standard forms required by the PDE module is detailed.The results were in good agreement with the literature,indicating that the PDE module provides a promising means to solve complex PDEs,especially for those a dedicated finite element module has yet to be developed.展开更多
This paper presents an efficient numerical technique for solving multi-term linear systems of fractional ordinary differential equations(FODEs)which have been widely used in modeling various phenomena in engineering a...This paper presents an efficient numerical technique for solving multi-term linear systems of fractional ordinary differential equations(FODEs)which have been widely used in modeling various phenomena in engineering and science.An approximate solution of the system is sought in the formof the finite series over the Müntz polynomials.By using the collocation procedure in the time interval,one gets the linear algebraic system for the coefficient of the expansion which can be easily solved numerically by a standard procedure.This technique also serves as the basis for solving the time-fractional partial differential equations(PDEs).The modified radial basis functions are used for spatial approximation of the solution.The collocation in the solution domain transforms the equation into a system of fractional ordinary differential equations similar to the one mentioned above.Several examples have verified the performance of the proposed novel technique with high accuracy and efficiency.展开更多
The deferred correction(DeC)is an iterative procedure,characterized by increasing the accuracy at each iteration,which can be used to design numerical methods for systems of ODEs.The main advantage of such framework i...The deferred correction(DeC)is an iterative procedure,characterized by increasing the accuracy at each iteration,which can be used to design numerical methods for systems of ODEs.The main advantage of such framework is the automatic way of getting arbitrarily high order methods,which can be put in the Runge-Kutta(RK)form.The drawback is the larger computational cost with respect to the most used RK methods.To reduce such cost,in an explicit setting,we propose an efcient modifcation:we introduce interpolation processes between the DeC iterations,decreasing the computational cost associated to the low order ones.We provide the Butcher tableaux of the new modifed methods and we study their stability,showing that in some cases the computational advantage does not afect the stability.The fexibility of the novel modifcation allows nontrivial applications to PDEs and construction of adaptive methods.The good performances of the introduced methods are broadly tested on several benchmarks both in ODE and PDE contexts.展开更多
目的将实时直接分析离子源(direct analysis in real time,DART)与三重四极杆质谱联用,建立食品中非法添加PDE-5型抑制剂的快速筛查方法。方法3种不同基质样品加入乙腈振摇10 s后,设进样速率0.2 mm/s,进样体积4μl,选择DART离子源,离子...目的将实时直接分析离子源(direct analysis in real time,DART)与三重四极杆质谱联用,建立食品中非法添加PDE-5型抑制剂的快速筛查方法。方法3种不同基质样品加入乙腈振摇10 s后,设进样速率0.2 mm/s,进样体积4μl,选择DART离子源,离子化温度450℃,在正离子、多反应监测(MRM)下进行检测。结果该方法7种物质的检出限为0.025~12.5μg/g,检出阳性样品4种,分别非法添加羟基卡巴地那非、环己基去甲他达拉非、N-苄基他达拉非和N-苯基丙氧苯基卡巴地那非。结论该方法样品前处理简单,分析速度快,定性准确,环境污染小,能满足食品中非法添加PDE-5型抑制剂的快速筛查要求。展开更多
基金supported by the National Natural Science Foundations of China(Grant Nos.12372073 and U20B2013)the Natural Science Basic Research Program of Shaanxi(Program No.2023-JC-QN-0030).
文摘A numerical approach is an effective means of solving boundary value problems(BVPs).This study focuses on physical problems with general partial differential equations(PDEs).It investigates the solution approach through the standard forms of the PDE module in COMSOL.Two typical mechanics problems are exemplified:The deflection of a thin plate,which can be addressed with the dedicated finite element module,and the stress of a pure bending beamthat cannot be tackled.The procedure for the two problems regarding the three standard forms required by the PDE module is detailed.The results were in good agreement with the literature,indicating that the PDE module provides a promising means to solve complex PDEs,especially for those a dedicated finite element module has yet to be developed.
基金funded by the National Key Research and Development Program of China(No.2021YFB2600704)the National Natural Science Foundation of China(No.52171272)the Significant Science and Technology Project of the Ministry of Water Resources of China(No.SKS-2022112).
文摘This paper presents an efficient numerical technique for solving multi-term linear systems of fractional ordinary differential equations(FODEs)which have been widely used in modeling various phenomena in engineering and science.An approximate solution of the system is sought in the formof the finite series over the Müntz polynomials.By using the collocation procedure in the time interval,one gets the linear algebraic system for the coefficient of the expansion which can be easily solved numerically by a standard procedure.This technique also serves as the basis for solving the time-fractional partial differential equations(PDEs).The modified radial basis functions are used for spatial approximation of the solution.The collocation in the solution domain transforms the equation into a system of fractional ordinary differential equations similar to the one mentioned above.Several examples have verified the performance of the proposed novel technique with high accuracy and efficiency.
文摘The deferred correction(DeC)is an iterative procedure,characterized by increasing the accuracy at each iteration,which can be used to design numerical methods for systems of ODEs.The main advantage of such framework is the automatic way of getting arbitrarily high order methods,which can be put in the Runge-Kutta(RK)form.The drawback is the larger computational cost with respect to the most used RK methods.To reduce such cost,in an explicit setting,we propose an efcient modifcation:we introduce interpolation processes between the DeC iterations,decreasing the computational cost associated to the low order ones.We provide the Butcher tableaux of the new modifed methods and we study their stability,showing that in some cases the computational advantage does not afect the stability.The fexibility of the novel modifcation allows nontrivial applications to PDEs and construction of adaptive methods.The good performances of the introduced methods are broadly tested on several benchmarks both in ODE and PDE contexts.
文摘目的将实时直接分析离子源(direct analysis in real time,DART)与三重四极杆质谱联用,建立食品中非法添加PDE-5型抑制剂的快速筛查方法。方法3种不同基质样品加入乙腈振摇10 s后,设进样速率0.2 mm/s,进样体积4μl,选择DART离子源,离子化温度450℃,在正离子、多反应监测(MRM)下进行检测。结果该方法7种物质的检出限为0.025~12.5μg/g,检出阳性样品4种,分别非法添加羟基卡巴地那非、环己基去甲他达拉非、N-苄基他达拉非和N-苯基丙氧苯基卡巴地那非。结论该方法样品前处理简单,分析速度快,定性准确,环境污染小,能满足食品中非法添加PDE-5型抑制剂的快速筛查要求。
