An efficient Sinc-collocation method via the DE transformation for eighth-order boundary value problems

被引：5

作者：

Qiu, Wenlin ^{[1
]}

Xu, Da ^{[1
]}

Zhou, Jun ^{[2
]}

Guo, Jing ^{[1
]}

机构：

[1] Hunan Normal Univ, Sch Math & Stat, Key Lab Comp & Stochast Math, Minist Educ, Changsha 410081, Hunan, Peoples R China

[2] Cent South Univ Forestry & Technol, Inst Math & Phys, Coll Sci, Changsha 410004, Hunan, Peoples R China

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2022年 / 408卷

基金：

中国国家自然科学基金;

关键词：

Non-linear eighth-order BVPs; Sinc method; DE transformation; Exponential convergence; Arbitrary even order; DOUBLE-EXPONENTIAL TRANSFORMATION; GALERKIN METHOD; EQUATION;

D O I：

10.1016/j.cam.2022.114136

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper shows the exponential convergence of the Sinc-collocation method based on the double exponential (DE) transformation applied to eighth-order boundary value problems (BVPs). Then using Kantorovich's theorem, we obtain the exponential convergence of the non-linear eighth-order ordinary differential equation (ODE). Furthermore, we extend the analytical results to the arbitrary even-order case. In the numerical experiment, several linear and nonlinear examples are provided to verify our theoretical analysis. Meanwhile, the solution yielded via DE transformation is compared with those obtained by single exponential (SE) transformation and existing method to demonstrate the high efficiency and accuracy of our method. (c) 2022 Elsevier B.V. All rights reserved.

引用

页数：20

共 37 条

[1] Agarwal R.P, 1986, BOUND VALUE PROBL
[2] ON COUPLED BENDING AND TORSIONAL VIBRATION OF UNIFORM BEAMS
BISHOP, RED
CANNON, SM
MIAO, S
[J]. JOURNAL OF SOUND AND VIBRATION, 1989, 131 (03) : 457 - 464
[3] FINITE-DIFFERENCE METHODS FOR THE SOLUTION OF SPECIAL 8TH-ORDER BOUNDARY-VALUE-PROBLEMS
BOUTAYEB, A
TWIZELL, EH
[J]. INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 1993, 48 (1-2) : 63 - 75
[4] Chandrasekhar S., 1981, Hydrodynamic and Hydromagnetic Stability
[5] El-Gamel M, 2004, MATH COMPUT, V73, P1325
[6] El-Gamel M., 2019, SEMA J, V76, P249, DOI [10.1007/s40324-018-0172-2, DOI 10.1007/S40324-018-0172-2]
[7] Application of homotopy perturbation method for solving eighth-order boundary value problems
Golbabai, A.
Javidi, M.
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2007, 191 (02) : 334 - 346
[8] Grenander U., 1958, CALIFORNIA MONOGRAPH
[9] Numerical solutions of eighth order BVP by the Galerkin residual technique with Bernstein and Legendre polynomials
Islam, Md. Shafiqul
Hossain, Md. Bellal
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2015, 261 : 48 - 59
[10] Kantorovich L. V., 1948, USPEHI MATEM NAUK NS, V3, P89

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