A Fast and Accurate Numerical Method for Solving Nonlinear Fourth-Order Boundary Value Problems in the Beam Theory

Abstract

In this paper, an efficient computational discretization approach is investigated for nonlinear fourth-order boundary value problems using beam theory. We specifically deal with nonlinear models described by fourth-order boundary value problems. The proposed method is applied on three different types of problems, i.e., the problem when an elastic bearing is non-zero (Case I), the problem under homogeneous boundary conditions of the unknown function and its second derivative (Case II), and the problem with integral boundary conditions (Case III). Moreover, the convergence analysis of the proposed method is provided. Finally, illustrative examples are included to demonstrate the applicability and validity of the technique and the comparison is made with the existing methods to show the efficiency and accuracy of the proposed method.

Keywords

• nonlinear fourth-order boundary value problem
• elastic beam equation
• hinged beam
• numerical method
• orthogonal collocation method