Firstly, an approach is presented for computing the adjoint operator vector of a class of nonlinear (i. e. partial-nonlinear) operator matrix by generalizing the method presented by Zhang et al. and the conjugate operators. Secondly, a united theory is given for solving a class of nonlinear (i. e. partial-nonlinear and including all linear) and non-homogeneous differential equations by the mathe-matics-mechanization method. In other words, a transformation is constructed by homogenization and triangulation which can reduce the original system to the simpler one which is diagonal. Finally, some practical applications are given in elasticity equations.
ZHANG Hong-qing,MEI Jian-qin.The computational differential algebraic geometrical method of constructing the fundamental solutions of system of PDEs[A].Proceeding of the 5th UK Conference on Boundary Integral Methods[C].Liverpool: Liverpool University Press, 2005,82-89.
ZHANG Hong-qing,FAN En-gui.Application of mechanical methods to partial differential equations[A].In:Wang D M,Gao X S,Eds.Mathematics Mechanization and Applications[C].London: Academic Press, 2000,409-539.