Finite element method (FEM) is an efficient numerical tool for the solution of partial differential equations (PDEs). It is one of the most general methods when compared to other numerical techniques. PDEs posed in a ...Finite element method (FEM) is an efficient numerical tool for the solution of partial differential equations (PDEs). It is one of the most general methods when compared to other numerical techniques. PDEs posed in a variational form over a given space, say a Hilbert space, are better numerically handled with the FEM. The FEM algorithm is used in various applications which includes fluid flow, heat transfer, acoustics, structural mechanics and dynamics, electric and magnetic field, etc. Thus, in this paper, the Finite Element Orthogonal Collocation Approach (FEOCA) is established for the approximate solution of Time Fractional Telegraph Equation (TFTE) with Mamadu-Njoseh polynomials as grid points corresponding to new basis functions constructed in the finite element space. The FEOCA is an elegant mixture of the Finite Element Method (FEM) and the Orthogonal Collocation Method (OCM). Two numerical examples are experimented on to verify the accuracy and rate of convergence of the method as compared with the theoretical results, and other methods in literature.展开更多
In this paper, a methodology for the numerical location of a global point-to-point (P2P for short) homoclinic asymptotically connecting orbit is applied to a modified version of Shimizu-Morioka system, which models a ...In this paper, a methodology for the numerical location of a global point-to-point (P2P for short) homoclinic asymptotically connecting orbit is applied to a modified version of Shimizu-Morioka system, which models a semiconductor laser. This type of global bifurcation can be considered as a stylized mathematical description of self-pulsation in this laser type, associ-ated with saturation. The location is achieved by use of a custom algorithm based on the method of orthogonal collocation on finite elements with fourth order boundary conditions, constructed through scale order approximations. The effectiveness of the algorithm and the superiority of high-order boundary conditions over the widely used first order ones are justified throughout the obtained graphical results.展开更多
In the present paper, a custom algorithm based on the method of orthogonal collocation on finite elements is presented and used for the location of global homoclinic point-to-point asymptotic connecting orbits. This k...In the present paper, a custom algorithm based on the method of orthogonal collocation on finite elements is presented and used for the location of global homoclinic point-to-point asymptotic connecting orbits. This kind of global bifurcation occurs in a large variety of problems in Applied Sciences, being associated to specific, significant physical aspects of the problem under consideration. In order to confront the difficulties faced when the location of such orbits is attempted, high order boundary conditions are constructed through scale order approximations, and used instead of the more common first order ones. The effectiveness of the implemented algorithm is justified by means of the specific applications and the figures presented.展开更多
具备快速电出力调节能力的热电联产(combined heat and power, CHP)机组能够提升工业园区电热耦合系统运行灵活性,促进新能源消纳,降低碳排放压力。采用微分方程形式建立CHP动态约束能够详细描述变量的变化情况,在调度中考虑动态约束能...具备快速电出力调节能力的热电联产(combined heat and power, CHP)机组能够提升工业园区电热耦合系统运行灵活性,促进新能源消纳,降低碳排放压力。采用微分方程形式建立CHP动态约束能够详细描述变量的变化情况,在调度中考虑动态约束能够掌握机组运行状态,降低事故风险。为此,以考虑碳交易过程的工业园区最小成本为目标,建立考虑CHP动态约束的工业园区低碳经济调度模型。然后基于序贯法框架,采用有限元正交配置法对模拟层的微分代数方程进行离散,并采用改进自适应差分进化算法求解优化层非线性规划问题。算例结果表明,有限元正交配置法能够以较少的离散点数获得较为精确的结果,提升了求解效率,验证了具备快速电出力调节能力的CHP机组能有效提升工业园区低碳经济水平。展开更多
文摘Finite element method (FEM) is an efficient numerical tool for the solution of partial differential equations (PDEs). It is one of the most general methods when compared to other numerical techniques. PDEs posed in a variational form over a given space, say a Hilbert space, are better numerically handled with the FEM. The FEM algorithm is used in various applications which includes fluid flow, heat transfer, acoustics, structural mechanics and dynamics, electric and magnetic field, etc. Thus, in this paper, the Finite Element Orthogonal Collocation Approach (FEOCA) is established for the approximate solution of Time Fractional Telegraph Equation (TFTE) with Mamadu-Njoseh polynomials as grid points corresponding to new basis functions constructed in the finite element space. The FEOCA is an elegant mixture of the Finite Element Method (FEM) and the Orthogonal Collocation Method (OCM). Two numerical examples are experimented on to verify the accuracy and rate of convergence of the method as compared with the theoretical results, and other methods in literature.
文摘In this paper, a methodology for the numerical location of a global point-to-point (P2P for short) homoclinic asymptotically connecting orbit is applied to a modified version of Shimizu-Morioka system, which models a semiconductor laser. This type of global bifurcation can be considered as a stylized mathematical description of self-pulsation in this laser type, associ-ated with saturation. The location is achieved by use of a custom algorithm based on the method of orthogonal collocation on finite elements with fourth order boundary conditions, constructed through scale order approximations. The effectiveness of the algorithm and the superiority of high-order boundary conditions over the widely used first order ones are justified throughout the obtained graphical results.
文摘In the present paper, a custom algorithm based on the method of orthogonal collocation on finite elements is presented and used for the location of global homoclinic point-to-point asymptotic connecting orbits. This kind of global bifurcation occurs in a large variety of problems in Applied Sciences, being associated to specific, significant physical aspects of the problem under consideration. In order to confront the difficulties faced when the location of such orbits is attempted, high order boundary conditions are constructed through scale order approximations, and used instead of the more common first order ones. The effectiveness of the implemented algorithm is justified by means of the specific applications and the figures presented.
文摘具备快速电出力调节能力的热电联产(combined heat and power, CHP)机组能够提升工业园区电热耦合系统运行灵活性,促进新能源消纳,降低碳排放压力。采用微分方程形式建立CHP动态约束能够详细描述变量的变化情况,在调度中考虑动态约束能够掌握机组运行状态,降低事故风险。为此,以考虑碳交易过程的工业园区最小成本为目标,建立考虑CHP动态约束的工业园区低碳经济调度模型。然后基于序贯法框架,采用有限元正交配置法对模拟层的微分代数方程进行离散,并采用改进自适应差分进化算法求解优化层非线性规划问题。算例结果表明,有限元正交配置法能够以较少的离散点数获得较为精确的结果,提升了求解效率,验证了具备快速电出力调节能力的CHP机组能有效提升工业园区低碳经济水平。
