For a given compactly supported scaling fun ct ion supported over [0,3]×[0,3], we present an algorithm to construct compac t ly supported orthogonal wavelets. By this algorithm, the symbol function of the associa...For a given compactly supported scaling fun ct ion supported over [0,3]×[0,3], we present an algorithm to construct compac t ly supported orthogonal wavelets. By this algorithm, the symbol function of the associated wavelets can be constructed explicitly.展开更多
The generalized algebraic method with symbolic computation is extended to some special-type nonlinear equations for constructing a series of new and more general travelling wave solutions in terms of special functions...The generalized algebraic method with symbolic computation is extended to some special-type nonlinear equations for constructing a series of new and more general travelling wave solutions in terms of special functions. Such equations cannot be directly dealt with by the method and require some kinds of pre-processing techniques. It is shown that soliton solutions and triangular periodic solutions can be established as the limits of the Jacobi doubly periodic wave solutions.展开更多
An improved algorithm for symbolic computation of Hirota bilinear form of nonlinear equations by a logarithm transformation is presented. The improved algorithm is more efficient by using the property of Hirota-D oper...An improved algorithm for symbolic computation of Hirota bilinear form of nonlinear equations by a logarithm transformation is presented. The improved algorithm is more efficient by using the property of Hirota-D operator. The software package HBFTrans2 is written in Maple and its running efficiency is tested by a variety of soliton equations.展开更多
In this paper, the extended symmetry of generalized variable-coeFficient Kadomtsev-Petviashvili （vcKP） equation is investigated by the extended symmetry group method with symbolic computation. Then on the basis of t...In this paper, the extended symmetry of generalized variable-coeFficient Kadomtsev-Petviashvili （vcKP） equation is investigated by the extended symmetry group method with symbolic computation. Then on the basis of the extended symmetry, we can establish relation among some different kinds of vcKP equations. Thus the exact solutions of these veKP equations can be constructed via the simple veKP equations or constant-coefficient KP equations.展开更多
Taking the (2+1)-dimensional Broer-Kaup-Kupershmidt system as a simple example, some families of rational form solitary wave solutions, triangular periodic wave solutions, and rational wave solutions are constructed b...Taking the (2+1)-dimensional Broer-Kaup-Kupershmidt system as a simple example, some families of rational form solitary wave solutions, triangular periodic wave solutions, and rational wave solutions are constructed by using the Riccati equation rational expansion method presented by us. The method can also be applied to solve more nonlinear partial differential equation or equations.展开更多
A new expanded approach is presented to find exact solutions of nonlinear differential-difference equations. As its application, the soliton solutions and periodic solutions of a lattice equation are obtained.
The expansion of the estimated stability region plays an important role in the stability analysis of nonlinear systems.However,current literatures have not provided a complete mathematical description for this problem...The expansion of the estimated stability region plays an important role in the stability analysis of nonlinear systems.However,current literatures have not provided a complete mathematical description for this problem.This paper reveals that essentially the enlargement or the compression of the estimated stability region results directly from the diffeomorphism map,which is induced by the flow contained in the stability region.By proving that any integration algorithm with an order higher than one can approximately trace the flow of the system,a generalized methodology is proposed to construct various algorithms to realize the enlargement or the compression of the estimated stability region.With this methodology,two new algorithms based on symbolic calculation are suggested to reduce the computational burden.Furthermore,this methodology is applied to construct a scalable numerical algorithm to calculate the critical clearing time(CCT) of the power system for given faults.Tests on the IEEE 10-machine 39-bus system show that the computational results coincide well with the step-by-step simulation with high accuracy.展开更多
Factorization of polynomials is one of the foundations of symbolic computation.Its applications arise in numerous branches of mathematics and other sciences.However,the present advanced programming languages such as C...Factorization of polynomials is one of the foundations of symbolic computation.Its applications arise in numerous branches of mathematics and other sciences.However,the present advanced programming languages such as C++ and J++,do not support symbolic computation directly.Hence,it leads to difficulties in applying factorization in engineering fields.In this paper,the authors present an algorithm which use numerical method to obtain exact factors of a bivariate polynomial with rational coefficients.The proposed method can be directly implemented in efficient programming language such C++ together with the GNU Multiple-Precision Library.In addition,the numerical computation part often only requires double precision and is easily parallelizable.展开更多
文摘For a given compactly supported scaling fun ct ion supported over [0,3]×[0,3], we present an algorithm to construct compac t ly supported orthogonal wavelets. By this algorithm, the symbol function of the associated wavelets can be constructed explicitly.
基金The project supported by the Natural Science Foundation of Shandong Province and the Natural Science Foundation of Liaocheng University
文摘The generalized algebraic method with symbolic computation is extended to some special-type nonlinear equations for constructing a series of new and more general travelling wave solutions in terms of special functions. Such equations cannot be directly dealt with by the method and require some kinds of pre-processing techniques. It is shown that soliton solutions and triangular periodic solutions can be established as the limits of the Jacobi doubly periodic wave solutions.
基金Supported by Scientific Research Fund of Zhejiang Provincial Education Department under Grant No.Y201017148the National Natural Science Foundations of China under Grant No.10735030+2 种基金the Natural Science Fund of Ningbo under Grant No.2009B21003the Scientific Research Fund of Ningbo University under Grant No.XKL09059the K.C.Wong Magana Fund in Ningbo University
文摘An improved algorithm for symbolic computation of Hirota bilinear form of nonlinear equations by a logarithm transformation is presented. The improved algorithm is more efficient by using the property of Hirota-D operator. The software package HBFTrans2 is written in Maple and its running efficiency is tested by a variety of soliton equations.
基金Supported by the National Natural Science Foundation of China under Grant No. 0735030Zhejiang Provincial Natural Science Foundations of China under Grant No. Y6090592+1 种基金National Basic Research Program of China (973 Program 2007CB814800)Ningbo Natural Science Foundation under Grant No. 2008A610017 and K.C. Wong Magna Fund in Ningbo University
文摘In this paper, the extended symmetry of generalized variable-coeFficient Kadomtsev-Petviashvili （vcKP） equation is investigated by the extended symmetry group method with symbolic computation. Then on the basis of the extended symmetry, we can establish relation among some different kinds of vcKP equations. Thus the exact solutions of these veKP equations can be constructed via the simple veKP equations or constant-coefficient KP equations.
文摘Taking the (2+1)-dimensional Broer-Kaup-Kupershmidt system as a simple example, some families of rational form solitary wave solutions, triangular periodic wave solutions, and rational wave solutions are constructed by using the Riccati equation rational expansion method presented by us. The method can also be applied to solve more nonlinear partial differential equation or equations.
基金the National Natural Science Foundation of China (No. 60773119)
文摘A new expanded approach is presented to find exact solutions of nonlinear differential-difference equations. As its application, the soliton solutions and periodic solutions of a lattice equation are obtained.
基金supported by the National Natural Science Foundation (Grant Nos 50525721, 50595411)
文摘The expansion of the estimated stability region plays an important role in the stability analysis of nonlinear systems.However,current literatures have not provided a complete mathematical description for this problem.This paper reveals that essentially the enlargement or the compression of the estimated stability region results directly from the diffeomorphism map,which is induced by the flow contained in the stability region.By proving that any integration algorithm with an order higher than one can approximately trace the flow of the system,a generalized methodology is proposed to construct various algorithms to realize the enlargement or the compression of the estimated stability region.With this methodology,two new algorithms based on symbolic calculation are suggested to reduce the computational burden.Furthermore,this methodology is applied to construct a scalable numerical algorithm to calculate the critical clearing time(CCT) of the power system for given faults.Tests on the IEEE 10-machine 39-bus system show that the computational results coincide well with the step-by-step simulation with high accuracy.
基金partly supported by the National Natural Science Foundation of China under Grant Nos.91118001 and 11170153the National Key Basic Research Project of China under Grant No.2011CB302400Chongqing Science and Technology Commission Project under Grant No.cstc2013jjys40001
文摘Factorization of polynomials is one of the foundations of symbolic computation.Its applications arise in numerous branches of mathematics and other sciences.However,the present advanced programming languages such as C++ and J++,do not support symbolic computation directly.Hence,it leads to difficulties in applying factorization in engineering fields.In this paper,the authors present an algorithm which use numerical method to obtain exact factors of a bivariate polynomial with rational coefficients.The proposed method can be directly implemented in efficient programming language such C++ together with the GNU Multiple-Precision Library.In addition,the numerical computation part often only requires double precision and is easily parallelizable.
