The Permanently Effective HPD To Solve A Kind Of Nonlinear Problems

Since Zhong Wanxie,a well-known academician proposed the High Precision Direct(HPD) integration in 1994, this scheme, which is the academic intersect of computational mechanics, engineering application, computational mathematics has developed quickly and become an academic focus. However,there are many difficulties in devising the permanently effective HPD to solve nonlinear problems and non-homogeneous autonomy system, which lie on dealing with nonlinear terms and the inverse of the transfer matrix, besides this ,the computational time longer in ervery step.with a series of researches about HPD, non-homogeneous has got great breakthrough and developed except in nonlinear systems, and any means of this problem is not satisfied.Firstly, This paper summaried the 4 inherent rules of HPD, has discussed HPD about a kind of two-order non-linear partial differential equation (NB-PDE) based on these rules, and has carried out a series of researches.This article has mainly five innovations and ten points as following:1) Summaried the 4 inherent rules of HPD.2) Proposed the concept of, in order to transform NB-PDEε- eunceasingly for the scheme of original HPD .3) Follows the inherent rule 2, transform NB-PDEε- eunceasingly for non- linear ODES with only one variable with wavelet methods, details as follows:a. Proposed the wavelet mixed basis based on wavwlet scale basis.b. Proposed the connection coefficients of the wavelet model.c. Proved the wavelet filter coefficients may obtained by the proving with some schemes.d. Proved the rationality of the wavelet function taking for the basis function, established the auto-adaptedωconvex method (note:ω-AC), which the adjustment of is advantageous to the real solution,had proven the M-S method is its exceptional case.e. Established the error analysis theorey of auto-adaptedωconvex method, numerical example show this method more effective.4) Follows the inherent rule 3, illustration about present interval HPD has isadvantages in precision. (this method is called interval HPD, if the transfer matrix is differ with interval[t_k ,t_k+1] 5) Follows the inherent rule 4,a. Established long-term-effective HPD(SBHPD) within dealing with nonlinear...