Research on the numerical solution and dynamic properties of nonlinear fractional differential equations
Journal Title: Lifelong Education - Year 2018, Vol 7, Issue 2
Abstract
Fractional calculus is an important branch of mathematical analysis, which is specialized in the study of the mathematical properties and applications of arbitrary order integral and differential, and is the extension of the traditional integral calculus. At present, fractional integral and derivative operators are mainly used to calculate fractional calculus, among which the most famous ones are Riemann-Liouville fractional integral and derivative, Caputo fractional derivative, Grümwald-Letnikov fractional integral and derivative, etc. At present, the numerical algorithm of finite difference scheme is mainly used to solve the approximate solution of the equation, to solve the fractional differential equation. Through the finite difference of time fractional order or space fractional order, the approximate solution of the equation is obtained, and the stability, convergence and compatibility of the scheme are checked, and the convergence order and estimation error are calculated. At present, the theory and method of nonlinear fractional differential equation are widely used in the study of various intermediate processes and critical phenomena in finance, physics and mechanics, which can better fit some natural physical processes and dynamic system processes.
Authors and Affiliations
Na Wang, Yanqin Yang
Keywords
Related Articles
- EP ID EP680237
- DOI -
- Views 125
- Downloads 0
The Government function in the development of life-long education and its revelation to China
Summary : The development of life-long education , from the introduction of ideas to the promotion of practice activities , is inseparable from the government's attention and Support . The role of the Japanese government...
The significance of promoting lifelong education system by MU class
business to Mu class on the basis of breaking the original form of school education , injects new energy into the building of a lifelong education system . mu-class open , scale , High Quality network course , Interactiv...
Study on the strategies of improving middle school English teachers' learning ability in the information age
With the deepening of education reform and the coming of information age, English information-based teaching has become the center of English teaching. At the same time, middle school English teachers must keep pace with...
Discussion on experimental teaching and cultivation of innovation ability
With the continuous progress of the society, China's demand for comprehensive high-quality talents is also increasing, so the reform and optimization of the new curriculum is an inevitable trend. The society has higher a...
The historical evolution of the theory of lifelong education
Summary : The theory of lifelong education enjoys a high rating in international education Theory , There are also many countries that attach great importance to lifelong education . The article makes a distinction betwe...