Numerical Simulation Of Differential Equations

Numerical simulation of the physical model is an important and useful way to deter-mine theoretical analysis of the model to correct or not. Numerical results play a greatguiding role in practical application. So looking for high-precision, high effciency andstable calculation method has important theoretical significance and value. We brieffydescribes the MEMS model and the vegetation model in this paper, then the backgroundabout the finite difference methods of knowledge is introduced.Secondly, We directly use forward Euler Difference scheme about equations of MEMSModel, but numerical results shock. So we changed the original equation into equivalentequations group forms, using Semi-implicit difference scheme, and the numerical results isvery good. In the paper, we also directly use central difference scheme with the originalequation in Two-order accuracy, and the result is also quite good, even the numericalresults of both formats are the same. In Vegetation Model paper, we mainly studiesvegetation changes state with the changing in the rate of mortality and the rate of rainfall.On the dimensionless ordinary differential equations, Papers using the explicit differencescheme for discrete. At last, we find the numerical results and actual state are the same.Thirdly,we have carried out a detailed analysis for the numerical results of eachdifference scheme, while each numerical results are the verification of theoretical resultsto correct or not.