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Dirac method for nonlinear and non-homogenous boundary value problems of plates
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作者 Xiaoye MAO Jiabin WU +2 位作者 Junning ZHANG Hu DING Liqun CHEN 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI CSCD 2024年第1期15-38,共24页
The boundary value problem plays a crucial role in the analytical investigation of continuum dynamics. In this paper, an analytical method based on the Dirac operator to solve the nonlinear and non-homogeneous boundar... The boundary value problem plays a crucial role in the analytical investigation of continuum dynamics. In this paper, an analytical method based on the Dirac operator to solve the nonlinear and non-homogeneous boundary value problem of rectangular plates is proposed. The key concept behind this method is to transform the nonlinear or non-homogeneous part on the boundary into a lateral force within the governing function by the Dirac operator, which linearizes and homogenizes the original boundary, allowing one to employ the modal superposition method for obtaining solutions to reconstructive governing equations. Once projected into the modal space, the harmonic balance method(HBM) is utilized to solve coupled ordinary differential equations(ODEs)of truncated systems with nonlinearity. To validate the convergence and accuracy of the proposed Dirac method, the results of typical examples, involving nonlinearly restricted boundaries, moment excitation, and displacement excitation, are compared with those of the differential quadrature element method(DQEM). The results demonstrate that when dealing with nonlinear boundaries, the Dirac method exhibits more excellent accuracy and convergence compared with the DQEM. However, when facing displacement excitation, there exist some discrepancies between the proposed approach and simulations;nevertheless, the proposed method still accurately predicts resonant frequencies while being uniquely capable of handling nonuniform displacement excitations. Overall, this methodology offers a convenient way for addressing nonlinear and non-homogenous plate boundaries. 展开更多
关键词 rectangular plate Dirac operator nonlinear boundary time-dependent boundary boundary value problem
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The Regularity of Solutions to Mixed Boundary Value Problems of Second-Order Elliptic Equations with Small Angles
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作者 Mingyu Wu 《Journal of Applied Mathematics and Physics》 2024年第4期1043-1049,共7页
This paper considers the regularity of solutions to mixed boundary value problems in small-angle regions for elliptic equations. By constructing a specific barrier function, we proved that under the assumption of suff... This paper considers the regularity of solutions to mixed boundary value problems in small-angle regions for elliptic equations. By constructing a specific barrier function, we proved that under the assumption of sufficient regularity of boundary conditions and coefficients, as long as the angle is sufficiently small, the regularity of the solution to the mixed boundary value problem of the second-order elliptic equation can reach any order. 展开更多
关键词 Mixed boundary value problems for Elliptic Equations Small-angle boundary value problems Regularity of Solutions to Elliptic Equations
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CAUCHY TYPE INTEGRALS AND A BOUNDARY VALUE PROBLEM IN A COMPLEX CLIFFORD ANALYSIS
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作者 曹南斌 李尊凤 +1 位作者 杨贺菊 乔玉英 《Acta Mathematica Scientia》 SCIE CSCD 2024年第1期369-385,共17页
Clifford analysis is an important branch of modern analysis;it has a very important theoretical significance and application value,and its conclusions can be applied to the Maxwell equation,Yang-Mill field theory,quan... Clifford analysis is an important branch of modern analysis;it has a very important theoretical significance and application value,and its conclusions can be applied to the Maxwell equation,Yang-Mill field theory,quantum mechanics and value problems.In this paper,we first give the definition of a quasi-Cauchy type integral in complex Clifford analysis,and get the Plemelj formula for it.Second,we discuss the H?lder continuity for the Cauchy-type integral operators with values in a complex Clifford algebra.Finally,we prove the existence of solutions for a class of linear boundary value problems and give the integral representation for the solution. 展开更多
关键词 Clifford analysis Cauchy type integral Plemelj formula Holder continuous boundary value problems
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Wavelet Multi-Resolution Interpolation Galerkin Method for Linear Singularly Perturbed Boundary Value Problems
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作者 Jiaqun Wang Guanxu Pan +1 位作者 Youhe Zhou Xiaojing Liu 《Computer Modeling in Engineering & Sciences》 SCIE EI 2024年第4期297-318,共22页
In this study,a wavelet multi-resolution interpolation Galerkin method(WMIGM)is proposed to solve linear singularly perturbed boundary value problems.Unlike conventional wavelet schemes,the proposed algorithm can be r... In this study,a wavelet multi-resolution interpolation Galerkin method(WMIGM)is proposed to solve linear singularly perturbed boundary value problems.Unlike conventional wavelet schemes,the proposed algorithm can be readily extended to special node generation techniques,such as the Shishkin node.Such a wavelet method allows a high degree of local refinement of the nodal distribution to efficiently capture localized steep gradients.All the shape functions possess the Kronecker delta property,making the imposition of boundary conditions as easy as that in the finite element method.Four numerical examples are studied to demonstrate the validity and accuracy of the proposedwavelet method.The results showthat the use ofmodified Shishkin nodes can significantly reduce numerical oscillation near the boundary layer.Compared with many other methods,the proposed method possesses satisfactory accuracy and efficiency.The theoretical and numerical results demonstrate that the order of theε-uniform convergence of this wavelet method can reach 5. 展开更多
关键词 Wavelet multi-resolution interpolation Galerkin singularly perturbed boundary value problems mesh-free method Shishkin node boundary layer
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Gradient Estimate of Solutions to a Class of Mean Curvature Equations with Prescribed Contact Angle Boundary Problem
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作者 Yuan Shengtong Han Fei 《数学理论与应用》 2024年第3期94-105,共12页
This paper studies the prescribed contact angle boundary value problem of a certain type of mean curvature equation.Applying the maximum principle and the moving frame method and based on the location of the maximum p... This paper studies the prescribed contact angle boundary value problem of a certain type of mean curvature equation.Applying the maximum principle and the moving frame method and based on the location of the maximum point,the boundary gradient estimation of the solutions to the equation is obtained. 展开更多
关键词 Moving frame Maximum principle Prescribed contact angle boundary value problem Mean curvature equation
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A Radial Basis Function Method with Improved Accuracy for Fourth Order Boundary Value Problems
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作者 Scott A. Sarra Derek Musgrave +1 位作者 Marcus Stone Joseph I. Powell 《Journal of Applied Mathematics and Physics》 2024年第7期2559-2573,共15页
Accurately approximating higher order derivatives is an inherently difficult problem. It is shown that a random variable shape parameter strategy can improve the accuracy of approximating higher order derivatives with... Accurately approximating higher order derivatives is an inherently difficult problem. It is shown that a random variable shape parameter strategy can improve the accuracy of approximating higher order derivatives with Radial Basis Function methods. The method is used to solve fourth order boundary value problems. The use and location of ghost points are examined in order to enforce the extra boundary conditions that are necessary to make a fourth-order problem well posed. The use of ghost points versus solving an overdetermined linear system via least squares is studied. For a general fourth-order boundary value problem, the recommended approach is to either use one of two novel sets of ghost centers introduced here or else to use a least squares approach. When using either ghost centers or least squares, the random variable shape parameter strategy results in significantly better accuracy than when a constant shape parameter is used. 展开更多
关键词 Numerical Partial Differential Equations boundary value problems Radial Basis Function Methods Ghost Points Variable Shape Parameter Least Squares
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Boundary Value Problems of p-Laplace Equations with Finite Time Delay
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作者 王宏洲 邓立虎 葛渭高 《Journal of Beijing Institute of Technology》 EI CAS 2001年第1期1-6,共6页
By establishing equivalent fixed point theorem, the boundary value problems of p Laplace equations with finite time delay are studied. It’s the first time that the functional differential equation is discussed w... By establishing equivalent fixed point theorem, the boundary value problems of p Laplace equations with finite time delay are studied. It’s the first time that the functional differential equation is discussed with p Laplacian. The topological degree and fixed point theorem on cone are used to prove the existence of solution and positive solution. The conditions are all easy to check. 展开更多
关键词 boundary value problem n Laplacian finite time delay fixed point
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Existence of Solutions for S-L Singular Boundary Value Problems with p-Laplacian Operators
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作者 郭彦平 葛渭高 单文锐 《Journal of Beijing Institute of Technology》 EI CAS 2002年第2期220-224,共5页
The existence of solutions for singular nonlinear two point boundary value problems subject to Sturm Liouville boundary conditions with p Laplacian operators is studied by the method of upper and lower solution... The existence of solutions for singular nonlinear two point boundary value problems subject to Sturm Liouville boundary conditions with p Laplacian operators is studied by the method of upper and lower solutions. The proof is based on an application of Schauder’s fixed point theorem to a modified problem whose solutions are that of the original one. At the same time, Arzela Ascoli theorem is used to prove that the defined operator N is a compact map. 展开更多
关键词 nonlinear boundary value problems p Laplacian operators fixed point upper solution lower solution
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Oscillatory Criteria for a Class of Boundary Value Problem of Nonlinear Hyperbolic Equations *L
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作者 王培光 葛渭高 《Journal of Beijing Institute of Technology》 EI CAS 1999年第1期20-24,共5页
Aim To study a class of boundary value problem of hyperbolic partial functional differential equations with continuous deviating arguments. Methods An averaging technique was used. The multi dimensional problem was... Aim To study a class of boundary value problem of hyperbolic partial functional differential equations with continuous deviating arguments. Methods An averaging technique was used. The multi dimensional problem was reduced to a one dimensional oscillation problem for ordinary differential equations or inequalities. Results and Conclusion The known results of oscillation of solutions for a class of boundary value problem of hyperbolic partial functional differential equations with discrete deviating arguments are generalized, and the oscillatory criteria of solutions for such equation with two kinds of boundary value conditions are obtained. 展开更多
关键词 continuous deviating arguments hyperbolic equation boundary value problem OSCILLaTION
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Existence of Multiple Positive Solutions for Higher-Order p-Laplacian Boundary Value Problems
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作者 贺小明 葛渭高 《Journal of Beijing Institute of Technology》 EI CAS 2002年第2期212-216,共5页
The existence of multiple positive solutions for a class of higher order p Laplacian boundary value problem is studied. By means of the Leggett Williams fixed point theorem in cones, existence criteria which e... The existence of multiple positive solutions for a class of higher order p Laplacian boundary value problem is studied. By means of the Leggett Williams fixed point theorem in cones, existence criteria which ensure the existence of at least three positive solutions of the boundary value problem are established. 展开更多
关键词 positive solutions cone Leggett Williams fixed point theorem p Laplacian boundary value problems
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A Class of Nonlocal Boundary Value Problems for Elliptic Systems in Unbounded Domains
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作者 莫嘉琪 张汉林 《Chinese Quarterly Journal of Mathematics》 CSCD 2001年第3期29-33,共5页
A class of nonlocal boundary value probl em s for elliptic systems in the unbounded domains are considered. Under suitable c onditions, the existence of solution and the comparison theorem for the boundary value prob... A class of nonlocal boundary value probl em s for elliptic systems in the unbounded domains are considered. Under suitable c onditions, the existence of solution and the comparison theorem for the boundary value problems are studied. 展开更多
关键词 elliptic system boundary value problem c omparison theorem
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Existence of Positive Solutions for Nonlinear Conjugate Boundary Value Problems
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作者 菅典兵 董正华 《Chinese Quarterly Journal of Mathematics》 CSCD 2002年第2期87-93,共7页
The present paper is concerned with the existence of positive solutions of the (k,n-k) conjugate boundary value problems(-1) n-k u (h) (t)=λa(t)f(u(t)),t∈(0,1), u (i) (0)=0,0≤i≤k-1, u (j) (0)=0,0... The present paper is concerned with the existence of positive solutions of the (k,n-k) conjugate boundary value problems(-1) n-k u (h) (t)=λa(t)f(u(t)),t∈(0,1), u (i) (0)=0,0≤i≤k-1, u (j) (0)=0,0≤j≤n-k-1,where λ is a positive parmeter. Krasnoselsii’s fixed point theorem is employed to obtain the existence criteria for positive solution. 展开更多
关键词 existence theorem positive solutions conjugate boundary value problem
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THE NONLINEAR BOUNDARY VALUE PROBLEM FOR k HOLOMORPHIC FUNCTIONS IN C^(2)
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作者 崔艳艳 李尊凤 +1 位作者 谢永红 乔玉英 《Acta Mathematica Scientia》 SCIE CSCD 2023年第4期1571-1586,共16页
k holomorphic functions are a type of generation of holomorphic functions.In this paper,a nonlinear boundary value problem for k holomorphic functions is primarily discussed on generalized polycylinders in C^(2).The e... k holomorphic functions are a type of generation of holomorphic functions.In this paper,a nonlinear boundary value problem for k holomorphic functions is primarily discussed on generalized polycylinders in C^(2).The existence of the solution for the problem is studied in detail with the help of the boundary properties of Cauchy type singular integral operators with a k holomorphic kernel.Furthermore,the integral representation for the solution is obtained. 展开更多
关键词 k holomorphic functions boundary value problems Cauchy type singular integral operators
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A Sparse Kernel Approximate Method for Fractional Boundary Value Problems
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作者 Hongfang Bai Ieng Tak Leong 《Communications on Applied Mathematics and Computation》 EI 2023年第4期1406-1421,共16页
In this paper,the weak pre-orthogonal adaptive Fourier decomposition(W-POAFD)method is applied to solve fractional boundary value problems(FBVPs)in the reproducing kernel Hilbert spaces(RKHSs)W_(0)^(4)[0,1] and W^(1)[... In this paper,the weak pre-orthogonal adaptive Fourier decomposition(W-POAFD)method is applied to solve fractional boundary value problems(FBVPs)in the reproducing kernel Hilbert spaces(RKHSs)W_(0)^(4)[0,1] and W^(1)[0,1].The process of the W-POAFD is as follows:(i)choose a dictionary and implement the pre-orthogonalization to all the dictionary elements;(ii)select points in[0,1]by the weak maximal selection principle to determine the corresponding orthonormalized dictionary elements iteratively;(iii)express the analytical solution as a linear combination of these determined dictionary elements.Convergence properties of numerical solutions are also discussed.The numerical experiments are carried out to illustrate the accuracy and efficiency of W-POAFD for solving FBVPs. 展开更多
关键词 Weak pre-orthogonal adaptive Fourier decomposition(W-POaFD) Weak maximal selection principle Fractional boundary value problems(FBVPs) Reproducing kernel Hilbert space(RKHS)
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THE ASYMPTOTIC BEHAVIOR OF SOLUTION FOR THE SINGULARLY PERTURBED INITIAL BOUNDARY VALUE PROBLEMS OF THE REACTION DIFFUSION EQUATIONS IN A PART OF DOMAIN
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作者 刘其林 莫嘉琪 《应用数学和力学》 EI CSCD 北大核心 2001年第10期1075-1080,共6页
A class of singularly perturbed initial boundary value problems for the reaction diffusion equations in a part of domain are considered. Using the operator theory the asymptotic behavior of solution for the problems i... A class of singularly perturbed initial boundary value problems for the reaction diffusion equations in a part of domain are considered. Using the operator theory the asymptotic behavior of solution for the problems is studied. 展开更多
关键词 奇摄动 反应扩散方程 初始边值问题 算子理论 渐近性态
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Matrix Boundary Value Problem on Hyperbola
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作者 Shaohua Fan 《Journal of Applied Mathematics and Physics》 2023年第4期884-890,共7页
We study a special class of lower trigonometric matrix value boundary value problems on hyperbolas. Firstly, the pseudo-orthogonal polynomial on hyperbola is given in bilinear form and it is shown that it is the only ... We study a special class of lower trigonometric matrix value boundary value problems on hyperbolas. Firstly, the pseudo-orthogonal polynomial on hyperbola is given in bilinear form and it is shown that it is the only one. Secondly, a special boundary value problem of lower triangular matrix is presented and transformed into four related boundary value problems. Finally, Liouville theorem and Painlevé theorem and pseudo-orthogonal polynomials are used to give solutions. 展开更多
关键词 HYPERBOLa Matrix boundary value problem Orthogonal Polynomial
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Efficient Decomposition Shooting Method for Solving Third-Order Boundary Value Problems
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作者 Nawal Al-Zaid Kholoud Alzahrani +1 位作者 Huda Bakodah Mariam Al-Mazmumy 《International Journal of Modern Nonlinear Theory and Application》 2023年第3期81-98,共18页
The present paper proposes a mathematical method to numerically treat a class of third-order linear Boundary Value Problems (BVPs). This method is based on the combination of the Adomian Decomposition Method (ADM) and... The present paper proposes a mathematical method to numerically treat a class of third-order linear Boundary Value Problems (BVPs). This method is based on the combination of the Adomian Decomposition Method (ADM) and, the modified shooting method. A complete derivation of the proposed method has been provided, in addition to its numerical implementation and, validation via the utilization of the Runge-Kutta method and, other existing methods. The method has been applied to diverse test problems and turned out to perform remarkably. Lastly, the simulated numerical results have been graphically illustrated and, also supported by some absolute error comparison tables. 展开更多
关键词 Linear Third Order BVPs Shooting Method adomian Decomposition Method Two-Point boundary value problem
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A CLASS OF NONLOCAL BOUNDARY VALUE PROBLEMS OF NONLINEAR ELLIPTIC SYSTEMS IN UNBOUNDED DOMAINS 被引量:64
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作者 莫嘉琪 欧阳成 《Acta Mathematica Scientia》 SCIE CSCD 2001年第1期93-97,共5页
The nonlocal boundary value problems for nonlinear elliptic systems in the unbounded domain are considered. Under suitable conditions the existence of solution and comparison theorem for the boundary value problems ar... The nonlocal boundary value problems for nonlinear elliptic systems in the unbounded domain are considered. Under suitable conditions the existence of solution and comparison theorem for the boundary value problems are studied. 展开更多
关键词 elliptic system boundary value problem comparison theorem
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ON SOLUTION OF A KIND OF RIEMANN BOUNDARY VALUE PROBLEM WITH SQUARE ROOTS 被引量:19
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作者 路见可 《Acta Mathematica Scientia》 SCIE CSCD 2002年第2期145-149,共5页
Solution of the Riemann boundary value problem with square roots (1.1) for analytic functions proposed in [1] is reconsidered, which was solved under certain assumptions on the branch points appeared. Here the work is... Solution of the Riemann boundary value problem with square roots (1.1) for analytic functions proposed in [1] is reconsidered, which was solved under certain assumptions on the branch points appeared. Here the work is continued without these assumptions and the problem is solved in the general case. 展开更多
关键词 Riemann boundary value problem branch points INDEX order at infinity sectionally holomorphic functions
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MULTIPLE POSITIVE SOLUTIONS OF SINGULAR THIRD-ORDER PERIODIC BOUNDARY VALUE PROBLEM 被引量:21
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作者 孙经先 刘衍胜 《Acta Mathematica Scientia》 SCIE CSCD 2005年第1期81-88,共8页
This paper deals with the singular nonlinear third-order periodic boundary value problem u'' + p(3)u = f (t, u), 0 less than or equal to t less than or equal to 2pi, with u((i)) (0) = u((i)) (2pi), i = 0, 1, 2... This paper deals with the singular nonlinear third-order periodic boundary value problem u'' + p(3)u = f (t, u), 0 less than or equal to t less than or equal to 2pi, with u((i)) (0) = u((i)) (2pi), i = 0, 1, 2, where p is an element of (Graphics) and f is singular at t = 0, t = 1 and u = 0. Under suitable weaker conditions than those of [1], it is proved by constructing a special cone in C[0, 2pi] and employing the fixed point index theory that the problem has at least one or at least two positive solutions. 展开更多
关键词 singular boundary value problem third-order differential system positive solution
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