Study On Numerical Algorithm For Fractional Bagley-Torvik Differential Equation Based On GA-Chebyshev Neural Network

In fluid mechanics,the fractional Bagley-Torvik differential equation is used to explain the motion of viscoelastic damping structures and fluid motion,as a general form of the fractional problem,this equation has been widely studied.However,acquire the exact solution of fractional Bagley-Torvik differential equation is so hard,accordingly,the research on numerical algorithm of fractional Bagley-Torvik differential equation is of important meaning in theoretical and actual applications,which provides an effective method for numerically solve of alike fractional differential equation and an advantageous tool for the mathematical modeling of complex systems.In this paper,based on the existing Chebyshev neural network,a new method using genetic algorithm to optimize Chebyshev neural network to solve the numerical solution of fractional Bagley-Torvik differential equation is proposed,and the initial value problem of fractional Bagley-Torvik differential equation is researched.Firstly,the ordinary expression of numerical solution satisfying the initial value condition is constructed combined with the Taylor expansion principle at the initial value point,and numerically solving the initial value problem of the above equation is transformed into solving the unconstrained minimization problem.Then,the error and convergence of the method are deduced theoretically according to Taylor expansion formula at the initial value point.Finally,numerical experiments verify that this method is feasible and effective for solving the above initial value problems.In this paper,the boundary value problem of fractional Bagley-Torvik differential equation is researched on the basis of the initial value problem.Firstly,the ordinary expression of numerical solution satisfying the boundary value condition is constructed combined with the Taylor expansion principle at boundary value points,and the original problem is transformed into solving the unconstrained minimization problem.Then,the error and convergence of the method are discussed theoretically according to the Taylor expansion formula at the boundary value points.Finally,the numerical results are compared with those of the existing numerical methods,the results show that this method is feasible and effective for solving the above boundary value problems.The results of this paper extend the theoretical research of the initial boundary value problem of fractional differential equation,enrich the numerical solution method of the initial boundary value problem of fractional differential equation,and provide a certain theoretical basis for the simulation of objective physics and mechanics problems.The paper has 15 figures,8 tables and 67 references.