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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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Existence of Positive Solution for Superlinear Semipositone Singular Second-order m-point Boundary Value Problem 被引量:4
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作者 ZHANG Xing-qiu 《Chinese Quarterly Journal of Mathematics》 CSCD 2010年第1期151-158,共8页
By applying fixed point theorem, the existence of positive solution is considered for superlinear semipositone singular m-point boundary value problem -(Lφ)(x)=(p(x)φ′(x))′+q(x)φ(x) and ξi ∈ (0,... By applying fixed point theorem, the existence of positive solution is considered for superlinear semipositone singular m-point boundary value problem -(Lφ)(x)=(p(x)φ′(x))′+q(x)φ(x) and ξi ∈ (0,1)with 0〈ξ1〈ξ2……〈ξm-2〈1,αi ∈ R^+,f ∈C[(0,1)×R^+,R^+],f(x,φ) may be singular at x=0 and x=1,g(x):(0,1)→R is Lebesgue measurable, g may tend to negative infinity and have finitely many singularities. 展开更多
关键词 SEMIPOSITONE SUPERLINEAR singular m-point boundary value fixed point theo-rem positive solution
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EXISTENCE OF POSITIVE SOLUTION TO SUPERLINEAR SEMIPOSITONE SINGULAR m-POINT BOUNDARY VALUE PROBLEMS 被引量:1
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作者 Zhang Xingqiu (School of Mathematics, Liaocheng University, Liaocheng 252059, Shandong) 《Annals of Differential Equations》 2008年第4期490-497,共8页
Sufficient conditions for the existence of positive solution to superlinear semi-positone singular m-point boundary value problem are given by cone expansion and compression theorem in norm type.
关键词 SEMIPOSITONE SUPERLINEAR singular m-point boundary value fixed point theorem positive solution
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The Singularly Perturbed Boundary Value Problems for Elliptic Equation with Turning Point 被引量:1
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作者 陈松林 莫嘉琪 《Chinese Quarterly Journal of Mathematics》 CSCD 2000年第3期12-16,共5页
The singularly perturbed elliptic equation boundary value problem with turning point is considered. Using the method of multiple scales and the comparison theorem, the asymptotic behavior of solution for the boundary ... The singularly perturbed elliptic equation boundary value problem with turning point is considered. Using the method of multiple scales and the comparison theorem, the asymptotic behavior of solution for the boundary value problem is studied. 展开更多
关键词 singular perturbation boundary value problem elliptic equation
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MULTIPLE SOLUTIONS FOR NONLINEAR SINGULAR m-POINT BOUNDARY VALUE PROBLEM IN ABSTRACT SPACE
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作者 Zhang Xingqiu 《Annals of Differential Equations》 2007年第2期243-252,共10页
By constructing a particular closed convex set and applying the Monch fixedpoint theorem, we study the existence of positive solution for a class of singular m-point boundary value problems.
关键词 singular equation fixed point positive solution m-point boundary value
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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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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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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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MULTIPLE POSITIVE SOLUTIONS TO SINGULAR BOUNDARY VALUE PROBLEMS FOR SUPERLINEAR SECOND ORDER ODES 被引量:11
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作者 蒋达清 《Acta Mathematica Scientia》 SCIE CSCD 2002年第2期199-206,共8页
This paper deals with the existence of positive solutions to the singular boundary value problemwhere q(t) may be singular at t = 0 and t = 1, f(t,y) may be superlinear at y =∞ and singular, at y = 0.
关键词 singular boundary value problem existence SUPERLINEAR the fixed point theorem
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A Class of Strongly Nonlinear Singular Perturbed Boundary Value Problems 被引量:15
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作者 TANG Rong-rong(Department of Mathematics, Huzhou Teacher’ s College, Huzhou 313000, China) 《Chinese Quarterly Journal of Mathematics》 CSCD 2003年第2期117-120,共4页
In this paper, a class of strongly nonlinear singular perturbed boundary value problems are coasidered by the theory of differential inequalities and the correction of boundary layer, under which the existence of solu... In this paper, a class of strongly nonlinear singular perturbed boundary value problems are coasidered by the theory of differential inequalities and the correction of boundary layer, under which the existence of solution is proved and the uniformly valid asymptotic expansions is obtained as well. 展开更多
关键词 nonlinear equation singular perturbation boundary value problem differential inequality
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THE SINGULARLY PERTURBED BOUNDARY VALUE PROBLEMS FOR HIGHER ORDER SEMILINEAR ELLIPTIC EQUATIONS 被引量:3
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作者 莫嘉琪 许玉兴 《Acta Mathematica Scientia》 SCIE CSCD 1997年第1期44-50,共7页
In this paper a singular perturbation of boundary value problem for elliptic partial differential equations of higher order is considered by using the differential inequalities. The uniformly valid asymptotic expansio... In this paper a singular perturbation of boundary value problem for elliptic partial differential equations of higher order is considered by using the differential inequalities. The uniformly valid asymptotic expansion in entire region is obtained. 展开更多
关键词 differential inequality singular perturbation asymptotic expansion elliptic partial differential equation boundary value problem
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The Shock Solution for a Class of Quasilinear Singularly Perturbed Boundary Value Problems 被引量:5
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作者 CHEN Ting YAO Jing-sun 《Chinese Quarterly Journal of Mathematics》 CSCD 2012年第3期317-322,共6页
The existence and asymptotic behavior of solution for a class of quasilinear singularly perturbed boundary value problems are discussed under suitable conditions by the theory of differential inequalities and matching... The existence and asymptotic behavior of solution for a class of quasilinear singularly perturbed boundary value problems are discussed under suitable conditions by the theory of differential inequalities and matching principle. 展开更多
关键词 QUASILINEAR boundary value problem singular perturbation
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A CLASS OF SINGULARLY PERTURBED NONLINEAR BOUNDARY VALUE PROBLEM 被引量:3
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作者 MoJiaqi LinWantao 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2005年第2期159-164,共6页
The singularly perturbed boundary value problem for the nonlinear boundary conditions is considered.Under suitable conditions,the asymptotic behavior of solution for the original problems is studied by using theory of... The singularly perturbed boundary value problem for the nonlinear boundary conditions is considered.Under suitable conditions,the asymptotic behavior of solution for the original problems is studied by using theory of differential inequalities. 展开更多
关键词 NONLINEAR singular perturbation boundary value problem.
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TWO POSITIVE SOLUTIONS TO THREE-POINT SINGULAR BOUNDARY VALUE PROBLEMS 被引量:3
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作者 李宇华 梁占平 《Acta Mathematica Scientia》 SCIE CSCD 2011年第1期29-38,共10页
In this article, we consider the existence of two positive solutions to nonlinear second order three-point singular boundary value problem: -u′′(t) = λf(t, u(t)) for all t ∈ (0, 1) subjecting to u(0) = ... In this article, we consider the existence of two positive solutions to nonlinear second order three-point singular boundary value problem: -u′′(t) = λf(t, u(t)) for all t ∈ (0, 1) subjecting to u(0) = 0 and αu(η) = u(1), where η ∈ (0, 1), α ∈ [0, 1), and λ is a positive parameter. The nonlinear term f(t, u) is nonnegative, and may be singular at t = 0, t = 1, and u = 0. By the fixed point index theory and approximation method, we establish that there exists λ* ∈ (0, +∞], such that the above problem has at least two positive solutions for any λ ∈ (0, λ*) under certain conditions on the nonlinear term f. 展开更多
关键词 Three-point singular boundary value problem positive solutions fixed point index
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SINGULAR PERTURBATION OF BOUNDARY VALUE PROBLEM FOR QUASILINEAR THIRD-ORDER ORDINARY DIFFERENTIAL EQUATIONS INVOLVING TWO SMALL PARAMETERS 被引量:2
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作者 林苏榕 田根宝 林宗池 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2001年第2期229-236,共8页
The singularly perturbed boundary value problem for quasilinear third-order ordinary differential equation involving two small parameters has been considered. For the three cases epsilon/mu (2) --> 0(mu --> 0), ... The singularly perturbed boundary value problem for quasilinear third-order ordinary differential equation involving two small parameters has been considered. For the three cases epsilon/mu (2) --> 0(mu --> 0), mu (2)/epsilon --> 0(epsilon --> 0) and epsilon = mu (2), the formal asymptotic solutions are constructed by the method of two steps expansions and the existences of solution are proved by using the differential inequality method. In addition, the uniformly valid estimations of the remainder term are given as well. 展开更多
关键词 two-parameters singular perturbation boundary value problem asymptotic expansion
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Existence Theory for Single and Multiple Positive Solutions to Singular Boundary Value Problems for Second-order Differential Systems P-Laplacian 被引量:4
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作者 ZHAO Xia HU Wei-min JIANG Da-qing 《Chinese Quarterly Journal of Mathematics》 CSCD 2013年第3期345-354,共10页
In this paper we present some new existence results for singular boundary value problems by Arzela-Ascoli theorem. In particular our nonlinearity may be singular in its dependent variable.
关键词 singular existence boundary value problem fixed point theorem in cones Arzela-Ascoli theorem
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POSITIVE SOLUTIONS OF BOUNDARY VALUE PROBLEMS FOR SECOND-ORDER SINGULAR NONLINEAR DIFFERENTIAL EQUATIONS 被引量:2
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作者 LI Ren-gui(李仁贵) +1 位作者 LI Li-shan(刘立山) 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2001年第4期495-500,共6页
New existence results are presented for the singular second-order nonlinear boundary value problems u ' + g(t)f(u) = 0, 0 < t < 1, au(0) - betau ' (0) = 0, gammau(1) + deltau ' (1) = 0 under the cond... New existence results are presented for the singular second-order nonlinear boundary value problems u ' + g(t)f(u) = 0, 0 < t < 1, au(0) - betau ' (0) = 0, gammau(1) + deltau ' (1) = 0 under the conditions 0 less than or equal to f(0)(+) < M-1, m(1) < f(infinity)(-)less than or equal to infinity or 0 less than or equal to f(infinity)(+)< M-1, m(1) < f (-)(0)less than or equal to infinity where f(0)(+) = lim(u -->0)f(u)/u, f(infinity)(-)= lim(u --> infinity)f(u)/u, f(0)(-)= lim(u -->0)f(u)/u, f(infinity)(+) = lim(u --> infinity)f(u)/u, g may be singular at t = 0 and/or t = 1. The proof uses a fixed point theorem in cone theory. 展开更多
关键词 second-order singular boundary value problems positive solutions cone fixed point
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MULTIPLE POSITIVE SOLUTIONS FOR SUPERLINEAR SECOND ORDER SINGULAR BOUNDARY VALUE PROBLEMS WITH DERIVATIVE DEPENDENCE 被引量:2
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作者 闫宝强 《Acta Mathematica Scientia》 SCIE CSCD 2008年第4期851-864,共14页
The existence of at least two positive solutions is presented for the singular second-order boundary value problem{1/p(t)( p(t)x′(t))′+Φ(t)f(t,x(t),p(t)x′(t))=0,0〈t〈1, limt→0 p(t)x′(t)=... The existence of at least two positive solutions is presented for the singular second-order boundary value problem{1/p(t)( p(t)x′(t))′+Φ(t)f(t,x(t),p(t)x′(t))=0,0〈t〈1, limt→0 p(t)x′(t)=0,x(1)=0by using the fixed point index, where f may be singular at x = 0 and px ′= 0. 展开更多
关键词 boundary value problems singularITY fixed point index
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Precise integration method for a class of singular two-point boundary value problems 被引量:2
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作者 Wen-Zhi Zhang Pei-Yan Huang 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2013年第2期233-240,共8页
In this paper we present a precise integration method based on high order multiple perturbation method and reduction method for solving a class of singular twopoint boundary value problems.Firstly,by employing the met... In this paper we present a precise integration method based on high order multiple perturbation method and reduction method for solving a class of singular twopoint boundary value problems.Firstly,by employing the method of variable coefficient dimensional expanding,the non-homogeneous ordinary differential equations(ODEs) are transformed into homogeneous ODEs.Then the interval is divided evenly,and the transfer matrix in every subinterval is worked out using the high order multiple perturbation method,and a set of algebraic equations is given in the form of matrix by the precise integration relation for each segment,which is worked out by the reduction method.Finally numerical examples are elaboratedd to validate the present method. 展开更多
关键词 singular two point boundary value problem Precise integration method High order multiple perturbation method Reduction method
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Singular Perturbations for a Class of Fourth-order Nonlinear Boundary Value Problem 被引量:2
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作者 LI Xu WANG Shi-peng 《Chinese Quarterly Journal of Mathematics》 CSCD 2011年第2期217-222,共6页
This paper is devoted to study the following the singularly perturbed fourth-order ordinary differential equation ∈y(4) =f(t,y',y'',y'''),0t1,0ε1 with the nonlinear boundary conditions y(0)=y'(1)=0,p... This paper is devoted to study the following the singularly perturbed fourth-order ordinary differential equation ∈y(4) =f(t,y',y'',y'''),0t1,0ε1 with the nonlinear boundary conditions y(0)=y'(1)=0,p(y''(0),y'''(0))=0,q(y''(1),y'''(1))=0 where f:[0,1]×R3→R is continuous,p,q:R2→R are continuous.Under certain conditions,by introducing an appropriate stretching transformation and constructing boundary layer corrective terms,an asymptotic expansion for the solution of the problem is obtained.And then the uniformly validity of solution is proved by using the differential inequalities. 展开更多
关键词 singular perturbation nonlinear boundary value problem differential inequality asymptotic expansion
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