The Solution of a Class of Third-Order Boundary Value Problems by the Reproducing Kernel Method

Homotopy Perturbation Method with Reproducing Kernel Method for Third Order Nonlinear Boundary Value Problems

This method is based on a combination of the homotopy perturbation method (HPM) and the reproducing kernel method (RKM). The main advantages of this method is that it can overcome the restriction of the form of nonlinearity term in differential equations and improve the iterative speed of homotopy perturbation method. The solution obtained using the method takes the form of a convergent series ...

Solutions of a Class of Sixth Order Boundary Value Problems Using the Reproducing Kernel Space

and Applied Analysis 3 Since i ∞ i=1 is dense in [0, 1], (Lu)(x) = 0, which implies that u ≡ 0 from the existence of L. Using reproducing kernel property, it can be written as i (x) = i (y) , x (y)⟩ = ⟨(L ∗ i (x) , x (y)⟩ = i (y) , x (y)⟩

Numerical Solution of Seventh Order Boundary Value Problems Using the Reproducing Kernel Space

Abstract: The aim of study of this article is to determine the solution of seventh order boundary value problem. The behavior of the induction motor is simulated by fifth order differential equation model and induction machine with two rotor circuits is represented by the seventh order differential equations. In this study, a Reproducing Kernel Method (RKM) for a class of seventh-order nonlinea...

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

The third-order boundary value problems arise in the study of draining and coating flows. In the past few years, third-order boundary value problems with various types of boundary conditions have been studied in many literatures. For details, see 1–6 and their references therein. In the last decade or so, several papers 7–12 have been devoted to the study of third-order differential equations w...

Solving the non linear system of third order boundary value problems by using He's homotopy perturbation method