Spectral Collocation Method And Convergence Analysis Of Time Fractional Korteweg-de Vries Equation

In recent years,the fractional partial differential equation has been widely concerned because of its wide application and high practicability.For example,in the fields of physics,engineering,biology,control theory and fluid dynamics,the fractional partial differential equation has been used in many aspects.Therefore,if we can solve its exact solution,we can get the exact solution,So far,researchers have achieved a lot of results in solving the classical Korteweg-de Vries(Kd V)equation,but the research of high-order nonlinear fractional Kd V equation is still in the initial stage,We consider introducing variables to transform the equation,so as to eliminate the singularity of the solution,and obtain good convergence on this basis.There are more detailed and systematic records about the development of spectral method in history and modern mathematics history.For differential equations,it is an important tool to calculate it.Based on this,we will consider the application of Jacobi spectral collocation method to discretize the equation.The main guiding idea of this project is to use the Jacobi spectral collocation method to solve the high-order spatiotemporal fractional order Kd V equation.The first step of this paper is to use the concept of Caputo,Riemann liouvville fractional derivative to transform the original equation into the second kind of Volterra type integral,which has a weak singular kernel.Then,the obtained integral is transformed linearly,The new form of Volterra integral can be obtained,the new integral is discretized in time and space by using the Jacobi spectral collocation method.Finally,the convergence of this method is analyzed and proved,and the error correlation between the approximate solution and the exact solution is obtained,In order to better verify the correctness of my theoretical analysis of this kind of equation,four numerical examples are given to prove that the Jacobi spectral collocation method is feasible for solving this equation...