[PDF] Top 20 New Implementation of Reproducing Kernel Method for Solving Functional Differential Equations

... 2009 Solving Singular Second Order Three-Point Boundary Value Problems Using Reproducing Kernel Hilbert Space Method.. 2012 A Numerical Solution to Nonlinear Second Order Three-Point Bou[r] ... See full document

... Reproducing kernel theory has important scientific applications in numerical analysis, ordinary and fractional differential equations, probability, statistics, and learning ...RKHS method for ... See full document

... ordinary differential equations play an impor- tant role in many ...a new algorithm for computing the solutions of singular second-order initial/boundary value problems (IBVPs) of the ... See full document

... in functional equations, such as ordinary or partial differential equations, integral and integral-differential equations ...a new Homotopy Perturbation Method ... See full document

... relatively new semi-analytical technique to approximate the solution of nonlinear multi-order fractional differential equations ...in reproducing kernel Hilbert space ...different ... See full document

... differential equations. Among these are the variational iteration method [– ], the Adomian descomposition method [, ], the fractional sub-equation method [–], the homotopy ... See full document

... for solving new generalized fractional order differential equations with linear functional argument is ...Tau method is extended to study this problem, where the derivatives are ... See full document

... block method in variable step. In a single integration step, two new approximates for the function y in (2) are obtained while keeping a constant stepsize, doubling or ...the method need to be ... See full document

... This paper is organized in six sections includ- ing the introduction. In the next section, Some preliminaries in fractional calculus are presented. Reproducing kernel space is defined in Section 3. ... See full document

... n method (RKM) has been a promising method the last decades, the reproducing kernel which applied more and more for solving vari- ous problems such as ordinary differential equa- ... See full document

... ence method [7], Galerkin [40], He’s variational iteration [15, 24, 27], homotopy analysis [12], homotopy perturbation [25], Laplace transform [10], reproducing kernel method [18], re- ... See full document

... proposed method. In section 3, we apply the reduced differential transform method to solve three test examples in order to show its ability and ... See full document

... a new numerical method for obtaining smooth approximations for solving ho- mogeneous and nonhomogeneous parabolic partial differential equations based on nonpolynomial cubic tension ... See full document

... collocation method is proposed for solving linear and nonlinear multi-order fractional differential equations based on the new definition of fractional derivative which is recently ... See full document

... Abstract— Reduced differential transform method (RDTM) is implemented for solving the linear and nonlinear Klein Gordon equations. The approximate analytical solution of the equation is ... See full document

... By the change of variables x = exp(–t) of the classical Mellin transform, one can obtain its Laplace transform. By using this connection with the two-side fuzzy Laplace transform, we can deduce the operator properties of ... See full document

... in solving ordinary differential equations ...Kutta method to gain the numerical solution while the absolute difference between them is known as the error in the ...Prince method ... See full document

... We organize this paper as follows: In Sect. 2, we give some basic definitions and use- ful lemmas. In Sect. 3, we introduce operational matrices of fractional integration based on fractional orthogonal basis functions. In ... See full document

... vector functional equations is obtained by the method of intersections, while in [2] several classes of homogeneous complex vector functional equations are solved on the basis of the ... See full document

... [9] S. Abbasbandy and A. Taati, “Numerical Solution of the System of Nonlinear Volterra Integro-Differential Equa- tions with Nonlinear Differential Part by the Operational Tau Method and Error ... See full document