scholarly journals Reproducing Kernel Space Method for the Solution of Linear Fredholm Integro-Differential Equations and Analysis of Stability

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Xueqin Lv ◽  
Yue Gao
Keyword(s):  
Differential Equation ◽  
Reproducing Kernel ◽  
Simple Algorithm ◽  
Approximate Solutions ◽  
Kernel Space ◽  
Reproducing Kernel Space ◽  
True Solution ◽  
Integro Differential Equation ◽  
Analysis Of Stability ◽  
Space Method

We present a numerical method to solve the linear Fredholm integro-differential equation in reproducing kernel space. A simple algorithm is given to obtain the approximate solutions of the equation. Through the comparison of approximate and true solution, we can find that the method can effectively solve the linear Fredholm integro-differential equation. At the same time the numerical solution of the equation is stable.

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 On Accuracy and Stability Analysis of the Reproducing Kernel Space Method for the Forced Duffing Equation

2016 ◽  
Vol 2016 ◽  
pp. 1-5
Author(s):  
Bahram Asadi ◽  
Taher Lotfi
Keyword(s):  
Reproducing Kernel ◽  
Boundary Integral ◽  
Duffing Equation ◽  
Stability And Convergence ◽  
Integral Conditions ◽  
Kernel Space ◽  
Reproducing Kernel Space ◽  
The Stability ◽  
Space Method ◽  
Accuracy And Stability

It is attempted to provide the stability and convergence analysis of the reproducing kernel space method for solving the Duffing equation with with boundary integral conditions. We will prove that the reproducing space method is stable. Moreover, after introducing the method, it is shown that it has convergence order two.

scholarly journals Iterative Reproducing Kernel Method for Solving Second-Order Integrodifferential Equations of Fredholm Type

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Iryna Komashynska ◽  
Mohammed AL-Smadi
Keyword(s):  
Reproducing Kernel ◽  
Kernel Method ◽  
Simple Algorithm ◽  
Approximate Solutions ◽  
Convergent Series ◽  
Second Order ◽  
Integrodifferential Equations ◽  
Reproducing Kernel Space ◽  
Fredholm Type ◽  
Reproducing Kernel Method

We present an efficient iterative method for solving a class of nonlinear second-order Fredholm integrodifferential equations associated with different boundary conditions. A simple algorithm is given to obtain the approximate solutions for this type of equations based on the reproducing kernel space method. The solution obtained by the method takes form of a convergent series with easily computable components. Furthermore, the error of the approximate solution is monotone decreasing with the increasing of nodal points. The reliability and efficiency of the proposed algorithm are demonstrated by some numerical experiments.

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