Numerical Algorithm For Solving Fractional Heat Conduction Equation And Its Paraller Implementation

Fractional heat conduction equation is a kind of diffusion equation whose space or time variable contains non-integer order derivative.However,the analytic solution of the type of diffusion equation is difficult to explicitly give,even if the answer of the simple linear equations also contain special functions,the calculation of these special functions is quite difficult.In view of this,the efficient numerical simulation of this kind of equation becomes the front problem in this field.Nowadays,the finite difference method,the finite element method,the spectral method and the series numerical solution approximation method of the fractional differential equation are studied.This paper takes time fractional heat conduction equation as the object of study.For the fractional differential equation of this kind,we choose the time definition of the appropriate fractional derivative in time derivative direction.The difference form in the direction of the left time derivative is obtained by the series approximation method.In the direction of the spatial derivative,the difference form of the right side is obtained by the numerical difference theory of the derivative integer derivative of maturity.In view of this,three effective finite difference algorithms for fractional differential equations of this kind are proposed,which are explicit difference scheme,implicit difference scheme and Crank-Nicholson difference scheme.Due to the non-locality of the solution of the fractional differential equation,it is necessary to store large amount of data in the process of numerical solution,and it is difficult to realize the process of numerical simulation.These problems will give us in the realization and understanding of fractional differential equations numerical solution caused great distress.Taking into account the numerical solution of the fractional differential equation in a large number of data exist in parallel,If the entire task,the use of data parallelism into multiple sub-tasks,the use of multiple processors to deal with the corresponding sub-tasks,And the coordination between the various processors,in order to get the experimental results,may be able to solve the numerical solution of differential equations in the calculation of large and large storage capacity of the problem.In this paper,three finite difference schemes for the fractional heat conduction equation of time are proposed.The finite difference of a given heat conduction equation is obtained,and the numerical and analytic solutions of the equation are compared.Three kinds of finite difference schemes are realized by numerical software.Two kinds of algorithm are given for the three difference schemes:The first is based on the C program under the CPU serial algorithm to achieve the second is to ensure that the results of the serial implementation of the calculation of the reliability and accuracy under the premise of improving the serial algorithm makes the program implementation process Is based on the GPU under the CUDA program parallel implementation.By comparing the time fractional heat conduction equation in different ways to achieve the process of operating speed,to illustrate the parallel algorithm is better than the way to achieve serial implementation of the algorithm.