The reproducing kernel method for nonlinear fourth-order BVPs-Reference-Cited by-同舟云学术

The reproducing kernel method for nonlinear fourth-order BVPs

Published:2023 Issue:11 Volume:8 Page:25371-25381
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Wang Shiyv¹,Lv Xueqin²,He Songyan³

Affiliation:

1. School of Mathematics and Sciences, Harbin Normal University, Harbin 150025, China

2. College of Basic Science, Tianjin Sino-German University of Applied Sciences, Tianjin 300350, China

3. School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, China

Abstract

<abstract><p>Based on the reproducing kernel theory, we solve the nonlinear fourth order boundary value problem in the reproducing kernel space $ W_{2}^{5}[0, 1] $. Its approximate solution is obtained by truncating the n-term of the exact solution and using the $ \varepsilon $-best approximate method. Meanwhile, the approximate solution $ u^{(i)}_{n}(x) $ converges uniformly to the exact solution $ u^{(i)}(x), (i, 0, 1, 2, 3, 4) $. The validity and accuracy of this method are verified by some examples.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

General Mathematics

Reference20 articles.

1. M. Ronto, A. M. Samoilenko, Numerical-analytic methods in the theory of boundary-value problems, World Scientific Publishing, 2001. https://doi.org/10.1142/3962

2. D. S. Dzhumabaev, S. M. Temesheva, A parametrization method for solving nonlinear two-point boundary value problems, Comput. Math. Math. Phys., 47 (2007), 37–61. https://doi.org/10.1134/S096554250701006X

3. D. S. Dzhumabaev, New general solutions of ordinary differential equations and the methods for the solutions of boundary-value problems, Ukr. Math. J., 71 (2019), 1006–1031. https://doi.org/10.1007/s11253-019-01694-9

4. R. Ma, J. Zhang, S. Fu, The method of lower and upper solutions for fourth-order two-point boundary value problems, J. Math. Anal. Appl., 215 (1997), 415–422. https://doi.org/10.1006/jmaa.1997.5639

5. D. Jiang, H. Z. Liu, X. J. Xu, Nonresonant singular fourth-order boundary value problems, Appl. Math. Lett., 18 (2005), 69–75. https://doi.org/10.1016/j.aml.2003.05.016