Purpose: In this paper, we shall present an algorithm for solving more general singular second-order multi-point boundary value problems.METHODs: The algorithm is based on the quasilinearization technique and the REPRODUCING KERNEL METHOD for linear multi-point boundary value problems.Results: Three numerical examples are given to demonstrate the efficiency of the present METHOD.Conclusions: Obtained results show that the present METHOD is quite efficient.

In the beginning, we describe the fuzzy inner product space and the fuzzy Hilbert space. Our goal is to use the fuzzy REPRODUCING KERNEL METHOD to solve the second-order fuzzy boundary value problem. The fuzzy convergence analysis of introduced METHOD is discussed in detail. We present some examples in the end.

The aim of this paper is to use the REPRODUCING KERNEL Hilbert Space METHOD (RKHSM) to solve the linear and nonlinear fuzzy impulsive fractional differential equations. Finding the numerical solutions of this class of equations are a difficult topic to analyze. In this study, convergence analysis, estimations error and bounds errors are discussed in detail under some hypotheses which provide the theoretical basis of the proposed algorithm. Some numerical examples indicate that this METHOD is an efficient one to solve the mentioned equations.

Purpose: In this paper, a new algorithm is presented for solving one-dimensional parabolic partial differential equations subject to integral conditions.METHODs: The algorithm is based on the transverse METHOD of lines and the REPRODUCING KERNEL METHOD. The transverse METHOD of lines can reduce a one-dimensional parabolic partial differential equation subject to integral conditions to a series of ordinary differential equations (ODEs) with integral boundary conditions. The REPRODUCING KERNEL METHOD is a relative new analytical technique, which can solve successfully ODEs with integral boundary conditions.Results: The present METHOD combines advantages of these two METHODs.Conclusions: Numerical results show that the present METHOD is quite efficient.