575 repeated eigenvalues. For this example, the ARIES software package produces results which are identical with those obtained by the Laplace transform method. The example serves to illustrate the validity of using (2. 2) to solve closed ARIES systems. The solution to the Markov chain presented in Fig. 2 and using the Transform method is given by the following set of expressions: p , (t) = e-(...

The titled problem of coupled thermoelasticity for porous structure has been solved with an instantaneous heat source acting on a plane area in an unbounded medium. The basic equations of thermoelasticity, after being converted into a one-dimensional form, have been written in the form of a vector-matrix differential equation and solved by the eigenvalue approach for the field variables in the ...

Algebraic techniques based on Laplace transform are widely used for solving differential equations and evaluating transfer of signals while analyzing physical aspects of many safety-critical systems. To facilitate formal analysis of these systems, we present the formalization of Laplace transform using the multivariable calculus theories of HOL-Light. In particular, we use integral, differentia...

Abstract: In this article, we develop a method to obtain approximate solutions of nonlinear coupled partial differential equations with the help of Laplace Decomposition Method (LDM). The technique is based on the application of Laplace transform to nonlinear coupled partial differential equations. The nonlinear term can easily be handled with the help of Adomian polynomials. We illustrate this...