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### Interpolated Coefficients Finite Element Method for Nonlinear Two-Point Boundary Value Problems

#### Author(s)

Lizheng Cheng 1, Hongping Li 1

#### Affiliation(s)

1 Institute of Primary Education, Changsha Normal University, Changsha, 410081, China

Hongping Li

#### ABSTRACT

In this paper, we consider nonlinear two-point boundary value problem using the Interpolated Coefficients Finite Element Method (ICFEM). We use the slice k-degree polynomial interpolation for nonlinear term and use Newton's method to solve the nonlinear equation system. We find the error convergence order of the ICFEM has some obvious characteristics. When k is an odd number, the error order is the normal finite element convergence order. And when k is an even number, the error convergence order has super convergence. The numerical results show the error convergence order of the 3rd ICFEM at the nodes is basically the normal finite element convergence order k + 1, and k = 2,4, the error convergence order of the 4th ICFEM at the node is generally higher than k + 1, almost reaching the 2k order super.

#### KEYWORDS

Finite element method, interpolated coefficients, nonlinear, convergence order

#### CITE THIS PAPER

Lizheng Cheng, Hongping Li, Interpolated Coefficients Finite Element Method for Nonlinear Two-Point Boundary Value Problems. Journal of Probability and Mathematical Statistics (2022) Vol. 2: 9-15. DOI: http://dx.doi.org/10.23977/jpms.2022.020102.