Computation Of The Inverse Problem Of A Kind Of Nonlinear Heat Conductivity Equation

The inverse problem of finding out heat conductivity of nonlinear heat conduction equation is mainly focused on in this paper.Because of the links among heat conductiv-ity,space and time,the nonlinear equations are firstly approximate converted into linear equations.Then,through discretization of central difference,we take use of marching method to obtain iterative equations about the temperature of grid nodes.Accodringly, numerical stability is discussed here.Finally,combing with generalized cross check(GCV) and the Tikhonov regularization method,the former thermal conductivity about space and temperature is worked out through inverse computation.Simulation numerical resluts show that the treatment is more feasible and efficacious. Full text is divided into four chapters:The first chapter introduces the background, development history and the related progress of the problem of heat conduction.at the same it also describes content and structure of this paper,outlines the research purpose of this study, content and meaning.Chapter Ⅱ Studies the difference discretization of the homogeneous nonlinear heat conduction equation and stability analysis of the discretized equation.The third chapter we has carried on the inverse numerical simulation combines with generalized cross check(GCV) and the Tikhonov regularization method。Here three numerical examples are given.In the fourth Chapter we summarize the full text.