THE AUTO-ADJUSTABLE DAMPING METHOD FOR SOLVING NONLINEAR EQUATIONS

The general approach for solving the nonlinear equations is linearizin g the equations and forming various iterative procedures, then executi ng the numerical simulation. For the strongly nonlinear problems, the solution obtained in the iterative process is always difficult, even d ivergent due to the numerical instability. It can not fulfill the engi neering requirements. Newton's method and its variants can not settle this problem. As a result, the application of numerical simulation for the strongly nonlinear problems is limited. An auto-adjustable dampin g method has been presented in this paper. This is a further improveme nt of Newton's method with damping factor. A set of vector of damping factor is introduced. This set of vector can be adjusted continuously during the iterative process in accordance with the judgement and adju stment. An effective convergence coefficient and quichening coefficien t are employed to relax the restricted requirements for the initial va lues and to shorten the iterative process. Then, the numerical stabili ty will be ensured for the solution of complicated strongly nonlinear equations. Using this method, some complicated strongly nonlinear heat transfer problems in airplanes and aeroengines have been numerically simulated successfully. It can be used for the numerical simulation of strongly nonlinear problems in engineering such as nonlinear hydrodyn amics and aerodynamics, heat transfer and structural dynamic response etc.