@article{Wang2023, 
author = {Shiyv Wang and Xueqin Lv and Songyan He},
title = {The reproducing kernel method for nonlinear fourth-order BVPs},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {11},
pages = {25371-25381},
keywords = {reproducing kernel space, nonlinear fourth-order BVPs, ε-best approximate solution},
url = {https://www.sciopen.com/article/10.3934/math.20231294},
doi = {10.3934/math.20231294},
abstract = {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    ε-best approximate method. Meanwhile, the approximate solution        u          n              (      i      )        (  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.}
}