Application of Lane-Emden differential equation numerical method in fair value analysis of financial accounting

Abstract

In order to study the fair value analysis of financial accounting, the Euler wavelet method is proposed to solve the numerical solutions of a class of Lane-Emden type differential equations with Dirichlet, Neumann and Neumann-Robin boundary conditions. The results show that the fractional integral formula of Euler wavelet function under the Riemann-Liouville fractional order definition and the L∞ and L2 errors of Haar wavelet are derived by the analytic form of Euler polynomial. By fixing M=4 and increasing the resolution scale k of Euler wavelet, a stable convergence solution can be obtained. The Lane-Emden equation with boundary conditions is transformed into algebraic equations by Euler wavelet collocation method, and the numerical results are compared with the results and exact solutions of other methods. The application advantages of fair value can be exerted through financial accounting to promote the transformation and upgrading of enterprises and realise the stable economic growth.

Parallelization of Runge–Kutta Methods for Hardware Implementation

“…Simulating continuous systems in discrete computers usually requires the numerical solution of ordinary differential equations (ODEs), which is usually performed using numerical integration methods [1][2][3][4]. Software implementing numerical integration methods is called an ODE solver.…”