Low cost numerical solution for three-dimensional linear and nonlinear integral equations via three-dimensional Jacobi polynomials

Sadri, K.1,2; Amini, A.3,4; Cheng, C.5,6

2017-08

10.1016/j.cam.2017.01.030

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS   影响因子和分区

0377-0427

1879-1778

In recent years, numerical methods have been introduced to solve two-dimensional Volterra and Fredholm integral equations. In this study, a numerical scheme is constructed to solve classes of linear and nonlinear three-dimensional integral equations (Volterra, Fredholm, and mixed Volterra Fredholm). This operational approach is proposed to easily and directly solve these equations at low computational costs. The scheme is based on the Jacobi polynomials on the interval [0, 1] where three-variable Jacobi polynomials are introduced and their operational matrices of integration and product are derived. Compared to other existing methods for multidimensional problems, the Jacobi operational method eliminates the time-consuming computations and solely employs the one-dimensional operational matrix to construct corresponding multidimensional operational matrices. The absolute error of the proposed method is almost constant on the studied interval even at higher dimensions, confirming the stability of the proposed operational Jacobi method. Required theorems on the convergence of the method are proved in Jacobi weighted Sobolev space. It is established that the error function vanishes as N increases. The method is evaluated using several illustrative examples which indicate the proposed method with lesser computational size compared to the Block Pulse functions, differential transform, and degenerate kernel methods. (C) 2017 Elsevier B.V. All rights reserved.

Three-dimensional integral equations Operational matrices Shifted Jacobi polynomials Convergence

SCI ; EI

英语

其他

Mathematics

Mathematics, Applied

WOS:000397362900033

ELSEVIER

20170803373153

Computation theory ; Integral equations ; Jacobian matrices ; Nonlinear equations ; Numerical methods ; One dimensional ; Sobolev spaces

Computer Theory, Includes Formal Logic, Automata Theory, Switching Theory, Programming Theory:721.1 ; Mathematics:921

MATHEMATICS

Web of Science

1.Islamic Azad Univ, Dept Math, Rasht Branch, POB 41335-3516, Rasht 4147654919, Iran
2.Islamic Azad Univ, Young Res Club, Rasht Branch, POB 41335-3516, Rasht 4147654919, Iran
3.Univ Western Sydney, Sch Comp Engn & Math, Kingswood Campus,Bld Y,Locked Bag 1797, Penrith, NSW 2751, Australia
4.Australian Coll Kuwait, Dept Mech Engn, Mishref, Kuwait
5.South Univ Sci & Technol, Dept Mat Sci & Engn, Shenzhen 518055, Peoples R China
6.South Univ Sci & Technol, Shenzhen Key Lab Nanoimprint Technol, Shenzhen 518055, Peoples R China

Sadri, K.,Amini, A.,Cheng, C.. Low cost numerical solution for three-dimensional linear and nonlinear integral equations via three-dimensional Jacobi polynomials[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS,2017,319:493-513.

Sadri, K.,Amini, A.,&Cheng, C..(2017).Low cost numerical solution for three-dimensional linear and nonlinear integral equations via three-dimensional Jacobi polynomials.JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS,319,493-513.

Sadri, K.,et al."Low cost numerical solution for three-dimensional linear and nonlinear integral equations via three-dimensional Jacobi polynomials".JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 319(2017):493-513.