scholarly journals Existence and Numerical Method for Nonlinear Third-Order Boundary Value Problem in the Reproducing Kernel Space

2010 ◽  
Vol 2010 (1) ◽  
pp. 459754 ◽  
Author(s):  
Xueqin Lü ◽  
Minggen Cui
Keyword(s):  
Boundary Value Problem ◽  
Numerical Method ◽  
Reproducing Kernel ◽  
Boundary Value ◽  
Kernel Space ◽  
Reproducing Kernel Space ◽  
Third Order

scholarly journals APPROXIMATE SOLUTION OF NONLINEAR MULTI-POINT BOUNDARY VALUE PROBLEM ON THE HALF-LINE

2012 ◽  
Vol 17 (2) ◽  
pp. 190-202 ◽  
Author(s):  
Jing Niu ◽  
Ying Zhen Lin ◽  
Chi Ping Zhang
Keyword(s):  
Approximate Solution ◽  
Boundary Value Problem ◽  
Reproducing Kernel ◽  
Boundary Value ◽  
Half Line ◽  
Point Boundary ◽  
Kernel Space ◽  
Reproducing Kernel Space ◽  
Uniformly Convergence ◽  
Reproducing Kernel Function

In this work, we construct a novel weighted reproducing kernel space and give the expression of reproducing kernel function skillfully. Based on the orthogonal basis established in the reproducing kernel space, an efficient algorithm is provided to solve the nonlinear multi-point boundary value problem on the half-line. Uniformly convergence of the approximate solution and convergence estimation of our algorithm are studied. Numerical results show our method has high accuracy and efficiency.

scholarly journals A Numerical Algorithm for Solving a Four-Point Nonlinear Fractional Integro-Differential Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
Er Gao ◽  
Songhe Song ◽  
Xinjian Zhang
Keyword(s):  
Analytical Solution ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Reproducing Kernel ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Value Problem ◽  
Kernel Space ◽  
Reproducing Kernel Space ◽  
Space Method ◽  
Term Approximation

We provide a new algorithm for a four-point nonlocal boundary value problem of nonlinear integro-differential equations of fractional orderq∈(1,2]based on reproducing kernel space method. According to our work, the analytical solution of the equations is represented in the reproducing kernel space which we construct and so then-term approximation. At the same time, then-term approximation is proved to converge to the analytical solution. An illustrative example is also presented, which shows that the new algorithm is efficient and accurate.

scholarly journals Theoretical and Numerical Aspects of a Third-order Three-point Nonhomogeneous Boundary Value Problem

2019 ◽  
Vol 20 (3) ◽  
pp. 417
Author(s):  
André L. M. Martinez ◽  
Marcelo R. A. Ferreira ◽  
Emerson V. Castelani
Keyword(s):  
Boundary Value Problem ◽  
Numerical Method ◽  
Positive Solutions ◽  
Boundary Value ◽  
Existence Results ◽  
Third Order ◽  
Nonhomogeneous Boundary ◽  
Point Equation

In this paper we are considering a third-order three-point equation with nonhomogeneous conditions in the boundary. Using Krasnoselskii's Theorem and Leray-Schauder Alternative we provide existence results of positive solutions for this problem. Nontrivials examples are given and a numerical method is introduced.

On J-self-adjoint operators with stable C-symmetries

2013 ◽  
Vol 143 (1) ◽  
pp. 141-167 ◽  
Author(s):  
Seppo Hassi ◽  
Sergii Kuzhel
Keyword(s):  
Symmetric Operator ◽  
Reproducing Kernel ◽  
Boundary Value ◽  
Functional Model ◽  
Kernel Space ◽  
Reproducing Kernel Space ◽  
Krein Spaces ◽  
Adjoint Operators

The paper is devoted to the development of the theory of self-adjoint operators in Krein spaces (J-self-adjoint operators) involving some additional properties arising from the existence of C-symmetries. We mainly focus on the recent notion of stable C-symmetry for J-self-adjoint extensions of a symmetric operator S. The general results involve boundary value techniques and reproducing kernel space methods, and they include an explicit functional model for the class of stable C-symmetries. Some of the results are specialized further by studying the case where S has defect numbers 〈2,2〉 in detail.

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