| On the basis of boundary value problem of differential equation,and similar construction theory of its solution is further explored.Firstly,solution structure of boundary value problem is studied and analyzed for a class of special composite differential equations,and structure of solution is expressed by continued fraction,namely similar structure,thus a new-style and simple method is put forward for solving this kind of boundary value problem: similar construction method,it is illustrated that similar construction method is applicable and simplicity for this class of problem at the same time.Secondly,aimed at multilayer composite reservoir,based on considering quadratic gradient term and not considering quadratic gradient term,seepage model is built under three kinds of outer conditions respectively.Definite solution problem of partial differential equation is transformed into boundary value problem of ordinary differential equation by linearization and Laplace transform,namely corresponding boundary value problem of composite modified Bessel equations;and it is solved by the proposed similar construction method,namely guide function is constructed by two linearly independent solutions of fixed solution equation,similar structure of solution is assembled by guide function and constructing similar kernel function.By further study and analysis,Its solution is expressed under three kinds of different outer conditions by unified formula,and corresponding between kernel function of solution is similar at the same time.Finally,some examples are enumerated and change curve of solution of corresponding differential equation is drawn by Matlab software,similar construction method is practical for compiling corresponding software of well test analysis,especially it is convenient for solving nonlinear seepage model,and it provides certain value for reference for perfecting similar construction theory that solving nonlinear seepage model at the same time. |
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