Differential Iterative Algorithm Based On Gradient Of Solving Stiff Ordinary Differential Equations

The initial value problem of stiff ordinary differential equation y’=f (y (t)) appears in automatic control, electronic networks, aviation Aerospace, nuclear reac-tions, celestial mechanics, biology, chemical reaction process,by using the approach of semi-discrete to partial differential equations and various types of evolution equation-s, it will also lead to such problems. So the tradional numerical methods of ordinary differential equations encounters great difficulties. To overcome the difficulty,the s-tudy of stiff ordinary equations is becoming one of the most active directions.The implicit Runge-Kutta method because of its high accuracy, good stability, is atten-tioned, but it because of the huge computation in practical condition is severely limited. How to reduce the amount of algebraic equations in Runge-Kutta method has been an important issue, but until now it has not been an effective solution, so we have to consider a special Runge-Kutta method, but the order of convergence of such methods is greatly reduced.The text of algebraic equations in Runge-Kutta method, proposes one differential interative algorithm based on gradient [8,9], and its theoretical analysis and research is proved to be effective by the numerical examples using this method with other parties.