Sinc-Galerkin method for solving linear sixth-order boundary-value problems

Abstract

Abstract. There are few techniques available to numerically solve sixth-order boundary-value problems with two-point boundary conditions. In this paper we show that the Sinc-Galerkin method is a very effective tool in numerically solving such problems. The method is then tested on examples with homogeneous and nonhomogeneous boundary conditions and a comparison with the modified decomposition method is made. It is shown that the Sinc-Galerkin method yields better results.

Solving the first Painleve equation using the Sinc-Galerkin method

“…Since then they have become increasingly popular and have been well studied. These methods have been used for solving many differential and integral equations [2,3,4,5,7,9,10,11,13,15,17,18]. Definitions, notation, and properties of Sinc functions and composite Sinc functions can be found in references [7,10].…”

Numerical Solution of Sixth-Order Differential Equations Arising in Astrophysics by Neural Network

“…This may be modeled by sixth-order boundary-value problems [4,5]. Numerical analysis literature proves that very little work has been conducted on finding the solution for sixth-order boundary-value problems [4][5][6][7][8]. A thorough discussion has been presented regarding theorems that list conditions for the existence and uniqueness of solutions of such problems in [9].…”

“…Another milestone was sixthorder differential equations by Twizell and Boutayeb [5]; they developed finite-difference methods of order two, four, six, and eight for the solution of problems as these. Authors in [8] gave rise to the Sinc-Galerkin method to solve sixth-order boundary-value problems. Wazwaz [22] used decomposition and modified domain decomposition methods for the same purpose and Bhrawy [23] put forward a spectral Legendre-Galerkin method to solve sixth-order boundary-value problems.…”

Improved Meshfree Approach to The Solution of Sixth Order Differential Equations

“…Siddiqi and Twizell used sixth-degree splines [8,9,10], where spline values at the mid knots of the interpolation interval and the corresponding values of the even order derivatives are related through consistency relations. M. E Gamel et al used Sinc-Galerkin method for the solutions of sixth order boundary-value problems [11]. Siraj-ul-islam et al solved Sixth-Order Boundary-Value Problems using Non-Polynomial Splines Approach [12] and Wazwaz [13,14] used decomposition and modified domain decomposition methods to explore solution of the sixth-order boundary-value problems.…”

“…Siraj-ul-islam et al solved Sixth-Order Boundary-Value Problems using Non-Polynomial Splines Approach [12] and Wazwaz [13,14] used decomposition and modified domain decomposition methods to explore solution of the sixth-order boundary-value problems. In this study, Element Free Galerkin (EFG) technique with Block Pulse Function (BPF) and Chebyshev wavelets (CW) based numerical integration is applied to obtain smooth approximations for the following boundary-value problem [11,13,15,17].…”