Some quadrature formulae for the numerical evaluation of singular integrals of arbitrary order are established and both the estimate of remainder and the convergence of each quadrature formula derived here are also gi...Some quadrature formulae for the numerical evaluation of singular integrals of arbitrary order are established and both the estimate of remainder and the convergence of each quadrature formula derived here are also given.展开更多
Based on the successive iteration in the Taylor series expansion method, a three-point explicit compact difference scheme with arbitrary order of accuracy is derived in this paper. Numerical characteristics of the sch...Based on the successive iteration in the Taylor series expansion method, a three-point explicit compact difference scheme with arbitrary order of accuracy is derived in this paper. Numerical characteristics of the scheme are studied by the Fourier analysisl Unlike the conventional compact difference schemes which need to solve the equation to obtain the unknown derivatives in each node, the proposed scheme is explicit and can achieve arbitrary order of accuracy in space. Application examples for the convectiondiffusion problem with a sharp front gradient and the typical lid-driven cavity flow are given. It is found that the proposed compact scheme is not only simple to implement and economical to use, but also is effective to simulate the convection-dominated problem and obtain high-order accurate solution in coarse grid systems.展开更多
The Peano derivatives are introduced for functions along an arc in the complex plane. Singular integrals of arbitrary order with singularities at its end-points are defined so that a unified theory for such integrals ...The Peano derivatives are introduced for functions along an arc in the complex plane. Singular integrals of arbitrary order with singularities at its end-points are defined so that a unified theory for such integrals and Cauchy principal value integrals is established.展开更多
We present a high-order Galerkin method in both space and time for the 1D unsteady linear advection-diffusion equation. Three Interior Penalty Discontinuous Galerkin (IPDG) schemes are detailed for the space discretiz...We present a high-order Galerkin method in both space and time for the 1D unsteady linear advection-diffusion equation. Three Interior Penalty Discontinuous Galerkin (IPDG) schemes are detailed for the space discretization, while the time integration is performed at the same order of accuracy thanks to an Arbitrary high order DERivatives (ADER) method. The orders of convergence of the three ADER-IPDG methods are carefully examined through numerical illustrations, showing that the approach is consistent, accurate, and efficient. The numerical results indicate that the symmetric version of IPDG is typically more accurate and more efficient compared to the other approaches.展开更多
The asymptotic behavior of solutions to certain integro-differential equation of arbitrary order is studied. Examples are given to illustrate the results.
The study of dynamic behaviour of nonlinear models that arise in ocean engineering play a vital role in our daily life.There are many examples of ocean water waves which are nonlinear in nature.In shallow water,the li...The study of dynamic behaviour of nonlinear models that arise in ocean engineering play a vital role in our daily life.There are many examples of ocean water waves which are nonlinear in nature.In shallow water,the linearization of the equations imposes severe conditions on wave amplitude than it does in deep water,and the strong nonlinear effects are observed.In this paper,q-homotopy analysis Laplace transform scheme is used to inspect time dependent nonlinear Lane-Emden type equation of arbitrary order.It offers the solution in a fast converging series.The uniqueness and convergence analysis of the considered model is presented.The given examples confirm the competency as well as accuracy of the presented scheme.The behavior of obtained solution for distinct orders of fractional derivative is dis-cussed through graphs.The auxiliary parameter¯h offers a suitable mode of handling the region of con-vergence.The outcomes reveal that the q-HATM is attractive,reliable,efficient and very effective.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
This paper presents a macroblock-level (MB-level) decoding and deblocking method for supporting the flexible macroblock ordering (FMO) and arbitrary slice ordering (ASO) bit streams in H.264 decoder and its SOC/ASIC i...This paper presents a macroblock-level (MB-level) decoding and deblocking method for supporting the flexible macroblock ordering (FMO) and arbitrary slice ordering (ASO) bit streams in H.264 decoder and its SOC/ASIC implementation. By searching the slice containing the current macroblock in the bit stream and switching slices correctly, MBs can be decoded in the raster scan order, while the decoding process can immediately begin as long as the slice containing the current MB is available. This architectural modification enables the MB-level decoding and deblocking 3-stage pipeline, and saves about 20% of SDRAM bandwidth. Implementation results showed that the design achieves real-time decoding of 1080HD (1920×1088@30 fps) at a system clock of 166 MHz.展开更多
This paper proposes a novel recursive partitioning method based on constrained learning neural networks to find an arbitrary number (less than the order of the polynomial) of (real or complex) roots of arbitrary polyn...This paper proposes a novel recursive partitioning method based on constrained learning neural networks to find an arbitrary number (less than the order of the polynomial) of (real or complex) roots of arbitrary polynomials. Moreover, this paper also gives a BP network constrained learning algorithm (CLA) used in root-finders based on the constrained relations between the roots and the coefficients of polynomials. At the same time, an adaptive selection method for the parameter d P with the CLA is also given. The experimental results demonstrate that this method can more rapidly and effectively obtain the roots of arbitrary high order polynomials with higher precision than traditional root-finding approaches.展开更多
We prove the existence of global attractors in H0^1 （Ω） for a nonclassical diffusion equation. Two types of nonlinearity f are considered： one is the critical exponent, and the other is the polynomial growth of ar...We prove the existence of global attractors in H0^1 （Ω） for a nonclassical diffusion equation. Two types of nonlinearity f are considered： one is the critical exponent, and the other is the polynomial growth of arbitrary order.展开更多
基金Supported by NNSF and RFDP of Higher Education of China.
文摘Some quadrature formulae for the numerical evaluation of singular integrals of arbitrary order are established and both the estimate of remainder and the convergence of each quadrature formula derived here are also given.
基金Project supported by the National Natural Science Foundation of China(No.50479053)
文摘Based on the successive iteration in the Taylor series expansion method, a three-point explicit compact difference scheme with arbitrary order of accuracy is derived in this paper. Numerical characteristics of the scheme are studied by the Fourier analysisl Unlike the conventional compact difference schemes which need to solve the equation to obtain the unknown derivatives in each node, the proposed scheme is explicit and can achieve arbitrary order of accuracy in space. Application examples for the convectiondiffusion problem with a sharp front gradient and the typical lid-driven cavity flow are given. It is found that the proposed compact scheme is not only simple to implement and economical to use, but also is effective to simulate the convection-dominated problem and obtain high-order accurate solution in coarse grid systems.
文摘The Peano derivatives are introduced for functions along an arc in the complex plane. Singular integrals of arbitrary order with singularities at its end-points are defined so that a unified theory for such integrals and Cauchy principal value integrals is established.
文摘We present a high-order Galerkin method in both space and time for the 1D unsteady linear advection-diffusion equation. Three Interior Penalty Discontinuous Galerkin (IPDG) schemes are detailed for the space discretization, while the time integration is performed at the same order of accuracy thanks to an Arbitrary high order DERivatives (ADER) method. The orders of convergence of the three ADER-IPDG methods are carefully examined through numerical illustrations, showing that the approach is consistent, accurate, and efficient. The numerical results indicate that the symmetric version of IPDG is typically more accurate and more efficient compared to the other approaches.
文摘The asymptotic behavior of solutions to certain integro-differential equation of arbitrary order is studied. Examples are given to illustrate the results.
文摘The study of dynamic behaviour of nonlinear models that arise in ocean engineering play a vital role in our daily life.There are many examples of ocean water waves which are nonlinear in nature.In shallow water,the linearization of the equations imposes severe conditions on wave amplitude than it does in deep water,and the strong nonlinear effects are observed.In this paper,q-homotopy analysis Laplace transform scheme is used to inspect time dependent nonlinear Lane-Emden type equation of arbitrary order.It offers the solution in a fast converging series.The uniqueness and convergence analysis of the considered model is presented.The given examples confirm the competency as well as accuracy of the presented scheme.The behavior of obtained solution for distinct orders of fractional derivative is dis-cussed through graphs.The auxiliary parameter¯h offers a suitable mode of handling the region of con-vergence.The outcomes reveal that the q-HATM is attractive,reliable,efficient and very effective.
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.
基金Project (No. 2002AA1Z1190) supported by the National Hi-Tech Research and Development Program (863) of China
文摘This paper presents a macroblock-level (MB-level) decoding and deblocking method for supporting the flexible macroblock ordering (FMO) and arbitrary slice ordering (ASO) bit streams in H.264 decoder and its SOC/ASIC implementation. By searching the slice containing the current macroblock in the bit stream and switching slices correctly, MBs can be decoded in the raster scan order, while the decoding process can immediately begin as long as the slice containing the current MB is available. This architectural modification enables the MB-level decoding and deblocking 3-stage pipeline, and saves about 20% of SDRAM bandwidth. Implementation results showed that the design achieves real-time decoding of 1080HD (1920×1088@30 fps) at a system clock of 166 MHz.
文摘This paper proposes a novel recursive partitioning method based on constrained learning neural networks to find an arbitrary number (less than the order of the polynomial) of (real or complex) roots of arbitrary polynomials. Moreover, this paper also gives a BP network constrained learning algorithm (CLA) used in root-finders based on the constrained relations between the roots and the coefficients of polynomials. At the same time, an adaptive selection method for the parameter d P with the CLA is also given. The experimental results demonstrate that this method can more rapidly and effectively obtain the roots of arbitrary high order polynomials with higher precision than traditional root-finding approaches.
基金Supported in part by the NSFC,Grant(10471056)Trans-Century Training Programme Foundation for the Talents of the State Education Commission
文摘We prove the existence of global attractors in H0^1 （Ω） for a nonclassical diffusion equation. Two types of nonlinearity f are considered： one is the critical exponent, and the other is the polynomial growth of arbitrary order.
