Uniqueness of system integration scheme of artificial intelligence technologyinfractional differential mathematical equation

• Autores: Yuming Chen, Jianfa Zhu, Liangxiao Li, Chengwen Long
• Localización: Applied Mathematics and Nonlinear Sciences, ISSN-e 2444-8656, Vol. 8, Nº. 1, 2023, págs. 1167-1176
• Idioma: inglés
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• Resumen

  • In order to explore the fractional differential equations in accounting informatization financial software, the author proposes a system for fractional diffusion wave equations and fractional differential equations, twonumerical algorithms with higher precision are given, and the amount of computation is reduced at the same time. First, based on the equivalent integral form of the time fractional diffusion wave equation, using the fractional echelon method and the Crank-Nicolson method, for the time fractional diffusion wave equation, a finite difference scheme is designed, this format has second-order accuracy in both the temporal and spatial directions and is computationally stable. Numerical examples verify the accuracy and effectiveness of this format. Thenwhen dealing with the initial value problem of fractional differential equations with Caputo derivative operator, convert it to the equivalent Voltera integral equation system, an initial approximate solution is obtained bya low-order method, derive the residual and error equations, the idea of applying the stepwise correction of spectral delay correction improves the numerical accuracy of the solution, at the same time, the Richard Askeyintegral equation is used to reduce the amount of calculation. At last, the high precision and effectiveness of the new method are verified by numerical experiments. Experiments show that: Starting from the equivalent integral form of the fractional diffusion wave equation, a second-order finite-difference scheme of the fractional-order diffusive wave equation is constructed, through numerical experiments, it is verified that the scheme has goodaccuracy and efficiency. In numerical solution, discrete integral equations have better numerical stability thandifferential equations, therefore, the format also has better stability. When taking different fractional derivative indices a=1.5 and a=1.8, it can be seen that the difference format constructed by the author, in the time direction, has second-order precision, as expected.