# Tag Archives: Laplace transform.

## An Analytical Method for Solving Wave Equations on Transmission Lines (Published)

Integral transform methods are very useful for solving problems in ordinary and partial differential equations. Among the integral transform methods, the Laplace transform has been applied to solve a lot of initial and boundary value problems in science and engineering. In this paper, the Laplace transform method was used for solving general wave equations on transmission lines. The model of general wave equations on transmission lines resulted into initial value hyperbolic second order partial differential equation which was transformed into ordinary differential equation by using the Laplace transform method. The method of variation of parameters and the convolution theorem of Laplace transformation was now applied to get the final solution to the problem.

## Characteristics of a System in Abnormal Weather Conditions by Using L Apl Ace Transforms (Published)

The research studies the availability and reliability to a system in which each unit of two modes, (normal, total failure) in two weather conditions- normal and stormy. To calculate reliability, the differential eq. of system resolved by Laplace Transform (L .T) depend on Complex imagine roots. Suppose the system rate of failure and rates of change of weather conditions are constant and the rate for repair of every unit are exponential distribution. The distribution of repair time be based on starting state of repair and not with the change in weather. we analysis graphically to watch the impress of several system parameters in mean time failure and availability.

## Reliability and Availability Analysis of Two–Dissimilar Units by Using Laplace Transforms (Published)

The paper studies the reliability and availability of two dissimilar units. In order to calculate reliability, a state dependent system can be converted into the system of first order ordinary differential equations based on Laplace Transform technique. The system of ordinary differential equations is solved using Inverse Laplace depend on Complex Conjugate roots. Let failure rate and repair rate of each unit are taken as an exponential distribution. Availability, reliability and the mean time to failure are derived. We analysis graphically to observe the effect of various systems Parameters on the availability system and mean time to failure.

## Binomial Mixture of Erlang Distribution (Published)

In this paper we introduce new Binomial  mixture distribution,  Binomial-Erlang Distribution( B-Er ) based on the transformation  where  on the interval [  0  , ∞ )  by using Moments methods and  Laplace transform  in mixing binomial distribution with Erlang distribution.