| Sumario: | The differential transform method (DTM) was introduced to solve linear and nonlinear
initial value problems which appear in electrical circuit analysis. In this method we
construct approximate solutions which is close to the exact solutions that differentiable
and having high accuracy with minor error. However, DTM is differ with the traditional
high order Taylor series where we need long computation time and derivatives. Thus
the DTM is applied to the high order differential equations as alternative way to get
Taylor series solution. In final stage this method yields truncated series solution in the
practical applications and most of time coincides with the Taylor expansion.
In this work we study the differential equations systems by using the differential transformation
method (DTM). Further, we apply the convolutions to matrices and study
their fundamental properties using differential transformation method. We also provide
many different applications of matrix convolutional equations such as coupled matrix
convolution equations by DTM. In the applications, we proved that the solutions converge
to the exact solutions. Finally we propose to generate matrix integro-differential
equations by using convolutions and differential equations.
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