Numerical method for solving the Dirichlet boundary value problem for nonlinear triharmonic equation

TL;DR

This paper introduces a fourth-order convergent numerical method for solving the nonlinear triharmonic Dirichlet boundary value problem by reducing it to an operator equation and employing an iterative approach.

Contribution

The paper develops a novel iterative method at both continuous and discrete levels for nonlinear triharmonic equations, demonstrating its high convergence order.

Findings

Method achieves fourth-order convergence.

Numerical examples validate the effectiveness of the approach.

Applicable to nonlinear triharmonic boundary problems.

Abstract

In this work, we consider the Dirichlet boundary value problem for nonlinear triharmonic equation. Due to the reduction of the nonlinear boundary value problem to operator equation for the nonlinear term and the unknown second normal derivative we design an iterative method at both continuous and discrete level for numerical solution of the problem. Some examples demonstrate that the numerical method is of fourth order convergence.