Visual Simulation for Numerical Solution of Fourth-Order Partial Differential Equations Based on the Improved Neural Network Algorithm

Abstract

The topic of this paper is to study the numerical solution of the fourth-order partial differential equation and analyze its visual application in software simulation. Therefore, for the initial circular domain, the expansion should be transformed into a fourth-order problem in the plane dimension. Then, we introduced appropriate-weighted Sobolev space based on the improved neural network algorithm and established a weak form and the corresponding discrete form for each one-dimensional fourth-order problem. The approximation properties of the cubic Hermite interpolation operator are used to verify the error value of the approximation solution. After obtaining the relevant algorithms, numerical empirical analysis is carried out to prove that the proposed algorithm is effective. Therefore, this article applies it to the visualization simulation technology, and the visualization module mainly completes two tasks: collecting geometric data and drawing models. At present, the application of the visualization module in the program mainly has two aspects: on the one hand, the boundary information of geometry can be obtained by screening the existing database so that the boundary model can be displayed in the visualization; on the other hand, from the calculation result file. Read the geometric information of particles and boundaries and perform dynamic simulation playback of the calculated results.