Research And Implementation Of Reconfigurable Universal Solver For Differential Equations

The initial value problem of ordinary differential equation is widely used in the description of the change law and motion phenomenon of things in various fields.With the increase of the depth and breadth of understanding of the objective world,the structure of differential equations in practical engineering applications is becoming more and more complex.The software implementation scheme has been unable to meet the strict constraints on the amount of calculation,calculation speed and accuracy of some applications.Therefore,it is of great practical value and application prospect to study the hardware design and implementation of numerical solutions of differential equations.At present,in the frontier research field of numerical solution technology for initial value problems of differential equations,scholars at home and abroad tend to implement the solution circuit of classical fourth-order Runge Kutta algorithm and other numerical solution algorithms on the field programmable gate array(FPGA)chip to complete the special differential equation solution under specific algorithms.Considering the requirements of generality,flexibility and efficiency in solving differential equations,this paper designs a reconfigurable universal solver for differential equations.By introducing reconfigurable technology into the structure design of the solver,the ability of the solver to customize the calculation path for differential equations and algorithms with different complexity is ensured.The designed solver supports the on-line reconstruction of the caculation structure of differential equations with different complexity,order,variables and other conditions,and has good versatility;at the same time,it can select the numerical solution algorithm according to the application requirements,and can adjust the initial value of input variables and change coefficient values on line,which has a good solution algorithm and flexibility;it supports the difference of initial solution conditions A large number of differential equations are solved simultaneously,which gives full play to the parallelism of hardware computing resources and reflects the high utilization of system resources.In this paper,the hardware implementation and verification of the designed differential equation solver are completed on FPGA platform,and the versatility,flexibility and efficiency of the solver are tested through several differential equation examples.Different numerical methods are used to solve different differential equations,and the generality of the solver is proved according to the accuracy of the result data.Different numerical methods are used to solve the same differential equation,and the flexibility of the solver is proved according to the accuracy of the result under different conditions and the difference of the calculation execution time.For the mass determination of differential equations under different initial conditions,the flexibility of the solver is proved by the speed-up ratio between software and hardware.