Application of Laplace Transform in Science and Engineering

One reliable mathematical tool that is used extensively in many scientific and technical fields is the Laplace transform (LP). Similar to the application of transfer functions in solving ordinary differential equations (ODEs), LPs offer a simple method for tackling increasingly complex engineering problems. LPs are used in physics and engineering, and this research first looks at such uses before concentrating on how they are used in electric circuit analysis. The research also explores more sophisticated uses, such as load frequency control in power systems engineering

HAAR WAVELET OPERATIONAL MATRIX BASED NUMERICAL INVERSION OF LAPLACE TRANSFORM FOR IRRATIONAL AND TRANSCENDENTAL TRANSFER FUNCTIONS

Irrational and transcendental functions can often be seen in signal processing or physical phenomena analysis as consequences of fractional-order and distributed-order models that result in fractional or partial differential equations. In cases when finding solution in analytical form tends to be difficult or impossible, numerical calculations such as Haar wavelet operational matrix method can be used.  Haar wavelet establishes a direct procedure for transfer function inversion using the wavelet operational matrix for orthogonal function set integration. In this paper an inverse Laplace transform of irrational and transcendental transfer functions using Haar wavelet operational matrix is proposed. Results for a number inverse Laplace transforms are numerically solved and compared with the analytical solutions and solutions provided by commonly used Invlap and NILT algorithms. This approach is useful when the original cannot be represented by an analytical formula and validity of the obtained result needs to be crosschecked and error estimated