LT-SCM-SNI method for solving definite solution problems of
three-interval composite nonlinear partial differential equations and
its application
Abstract
The definite solution problems of three-interval composite nonlinear
partial differential equations (PDE) under different conditions is
studied in the paper. Then the definite solution problems are solved by
Laplace transformation - similar constructing method - Stehfest
numerical inversion equation (LT-SCM-SNI method). Firstly, the definite
solution problems of three-interval composite nonlinear PDE is
transformed into the boundary value problems of three-interval composite
linear of ordinary differential equation (ODE) by linearization and
Laplace transformation (LT). Secondly, the solution in Laplace space of
the boundary value problems of three-interval composite linear of ODE is
obtained through using the similar constructing method (SCM). The
solution in real space of the definite solution problems of
three-interval composite nonlinear PDE is obtained through using the
Stehfest numerical inversion equation (SNI) and linearization equation.
Finally, the nonlinear spherical seepage model of three-interval
composite reservoir under infinite outer boundary conditions is solved
through using the LT-SCM-SNI method. The influence of various parameters
on dimensionless bottom-hole transient pressure is studied. The example
shows the simplicity and practicability of the method presented in the
paper.