Research on Definite Solution Problem of Partial Differential Equations
under Two Kinds of Elastic Coefficients of External Boundary Conditions
Abstract
This paper studies the definite solution problems of partial
differential equation (PDE) under two kinds of elastic coefficients
(exponential function type, polynomial function type) of external
boundary conditions. Then the definite solution problems are solved by
Laplace transformation, the method of undetermined coefficients and
Gaver-Stehfest numerical inversion equation. Firstly, the definite
solution problems of linear PDE are transformed into the boundary value
problems of linear differential equations in Laplace Space by Laplace
transformation. Secondly, the solutions in Laplace space of the boundary
value problems of linear differential equations are obtained through
using the method of undetermined coefficients. Finally, Obtain the real
space solution of the definite solution of PDE under three kinds of
elastic coefficients of external boundary conditions by using the
Gaver-Stehfest numerical inversion equation. According to the above
solution steps, this paper gives two different examples and obtains the
corresponding curve analysis of the definite solution problems of PDE
under two kinds of elastic coefficients of external boundary conditions.
The introduction of two kinds of elastic coefficients of external
boundary conditions not only expands the scope of the research on the
definite solution of PDE, but also improves the matching degree between
the theoretical model and the actual problems.