Searching the least value method for solving fourth-order nonlinear boundary value problems

Abstract

This paper obtains a searching least value (SLV) method for a class of fourth-order nonlinear boundary value problems is investigated. The argument is based on the reproducing kernel space $W_5[0,1]$. The approximate solutions $u_n\left(x\right)$ and $u_n^{\left(k\right)}\left(x\right)$ are uniformly convergent to the exact solution $u\left(x\right)$ and $u^{\left(k\right)}\left(x\right)(k=1,2,3,4)$ respectively. Numerical results are verified that the method is quite accurate and efficient for this kind of problem.