This paper presents a class of kernel-free boundary integral (KFBI) methods for general elliptic boundary value problems (BVPs). The boundary integral equations reformulated from the BVPs are solved iteratively with the GMRES method. During the iteration, the boundary and volume integrals involving Green's functions are approximated by structured grid-based numerical solutions, which avoids the...

The aim of this paper is to apply Galerkin weighted residual method for solving eleventh-order BVPs. In this method, we exploit Bernstein and Legendre polynomials as basis functions which are modified into to a new set of basis functions to satisfy the corresponding homogeneous form of boundary conditions where the essential types of boundary conditions are mentioned. The method is formulated a...

This numerical study exclusively focused on the direct two point diagonally multistep block method of order four (2DDM4) in form Adams-type formulas. The proposed predictor–corrector scheme was applied this to compute equally spaced solutions for third-order and multipoint boundary value problems (BVPs) subject Robin conditions concurrently at each step. optimization computational costs taken i...

We use basic results of general theory of …nite interpolation and linear algebra in order to prove the nonsingularity of a special class of centrosymmetric matrices arising in spectral methods in BVPs .

Abstract For nonlinear third-order three-point boundary value problems (BVPs), we develop two algorithms to find solutions, which automatically satisfy the specified conditions. We construct a shape function (BSF), is designed conditions and can be employed new by assigning different roles of free in BSF. In first algorithm, let functions complete BSFs bases solution, not only automatically, bu...

In this paper, we study the modified decomposition method (MDM) for solving nonlinear twopoint boundary value problems (BVPs) and show numerical experiments. The modified form of the Adomian decomposition method which is more fast and accurate than the standard decomposition method (SDM) was introduced by Wazwaz. In addition, we will compare the performance of the MDM and the new nonlinear shoo...

This paper investigates the existence and uniqueness of solutions to rst-order nonlinear boundary value problems (BVPs) involving fuzzy dif- ferential equations and two-point boundary conditions. Some sucient condi- tions are presented that guarantee the existence and uniqueness of solutions under the approach of Hukuhara dierentiability.