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A Stepwise Approach To Obtaining Solution To The Burridge
-
Knopoff Model
Accra Institu
te Of Technology
Accra
-
Ghana
The Burridge
-
knopoff model
=
-
Ř
-
(
-
)
is derived from the concept
of wave propagation. Various models have been derived from waves, however the difficulty is
how these various models can be solved either analytically
or numerically based on
mathematical principles. It is well known that most if not all wave models can be solved by
partial differential equation (PDE) and fourier series.
In this paper we proposed a solution method for the Burridge
-
knopoff model using wel
l
-
established analytical mathematical techniques.
We apply the method of separating variables to determine solution of the model by writing it in
the form as
(
,
)
=
(
)
(
)
which is two ordinary differential equations. This is a product
of two functions, each depending only on one of the variables
and
. Finally we used Fourier
series to ascertain that
the sum of finitely many solutions U
n
is a solu
tion of the model which reduces to
˛
˛
=
˛
˛
˛
,
we consider the infinite series
(
,
)
=
(
,
)
=
(
+
*
)
which satisfies the boundary conditions
(
0
,
)
=
0
,
(
,
)
=
0
as well as
two initial conditions
(
,
0
)
=
(
)
and
|
=
0
=
(
)
.
After going through these rigorous methods, it shows that