Authors :
Dr. Ismail Mohamed Abbas
Volume/Issue :
Volume 5 - 2020, Issue 11 - November
Google Scholar :
http://bitly.ws/9nMw
Scribd :
https://bit.ly/2JIkcHs
Abstract :
Current work on the numerical solution of
Laplace partial differential equation LPDE and of the
Poisson partial differential equation PPDE is based on
the replacement of the LPDE by an approximately
equivalent system of n linear algebraic equations. The
solution of this system has two distinct main approaches,
namely direct methods and indirect or iterative
techniques. In this article, we present a new statistical
method based on the chain of recurrence relations of the
so-called B matrix. Matrix B presents a chain recurrence
relation where an algorithm for numerical calculations is
simple.
The correctness and precision of the numerical
results are remarkable and superior to conventional
methods. The proposed stochastic matrix B and its series
of summations E are well defined and proven capable of
handling the diversity of situations in different domains
of LPDE and PPDE in 2D and 3D configurations such as
the study of electrostatic voltage in the Poisson problem
with Dirichlet boundary conditions. In this article, we
explain the underlying theory and discuss in detail some
2D and 3D applications of the new numerical method
Current work on the numerical solution of
Laplace partial differential equation LPDE and of the
Poisson partial differential equation PPDE is based on
the replacement of the LPDE by an approximately
equivalent system of n linear algebraic equations. The
solution of this system has two distinct main approaches,
namely direct methods and indirect or iterative
techniques. In this article, we present a new statistical
method based on the chain of recurrence relations of the
so-called B matrix. Matrix B presents a chain recurrence
relation where an algorithm for numerical calculations is
simple.
The correctness and precision of the numerical
results are remarkable and superior to conventional
methods. The proposed stochastic matrix B and its series
of summations E are well defined and proven capable of
handling the diversity of situations in different domains
of LPDE and PPDE in 2D and 3D configurations such as
the study of electrostatic voltage in the Poisson problem
with Dirichlet boundary conditions. In this article, we
explain the underlying theory and discuss in detail some
2D and 3D applications of the new numerical method
