| Summary: | 博士 === 國立成功大學 === 航空太空工程學系 === 86 === Differential transform and its application to engineering
problems, include initial-value problems, boundary-value
problems, and parameter identification problems are studied in
this theses. Since the operation of differential transform can
be developed from one dimension to multi-dimension, both ODE and
PDE can be solved by this technique. In some sense, differential
transform is more universal and practical than integral
transform. Differential transform method provides an adaptive
technique, which involved more concise adjustment policy and
raises the efficiency of numerical computation of initial-value
problems. Stiff equations can also be solved by this method with
specific stability and accuracy. Both linear and nonlinear
boundary-value problems can be solved as initial-value problems
after taking differential transform. From the problem
considered, it shows that the proposed technique can obtain
reasonably accurate approximate solutions and find all possible
solutions of the problem, which is distinct from the existing
approaches. Differential transform method is also applied to
parameter identification problems. The system model and the
criterion function can be obtained via the unknown parameter and
the initial value of state variable. The proposed method
provides direct search algorithm to find the maximum likelihood
estimate. Both linear and nonlinear problems can be solved in
the same process and the problem of singularity and sensitivity
in solving traditional inverse problems can be avoided.
|
|---|
