Application of the Elzaki Transform Iterative Method for the Fokker-Planck Equation (Published)
In this Paper, I propose a New Integral Transform which is still not widely known, nor used. The aim of the present paper is to investigate the application of the Elzaki Transform with combination of simple iteration Method for solving the Fokker-Planck equation and some similar equations. The method can easily be applied to many linear and non-linear Partial Differential Equations and is capable to reduce the size of computational work. In this approach the solution is found in the form of a convergent series with easily computed components. To give overview of Methodology, I have presented several examples in one- and two-dimensional cases.
Keywords: Elzaki Transform, Fokker-Planck Equation, Kolmogorov Equation, analytical solution.
Numerical Solution of Currents and Voltages Flow In Electrical Circuits (RLC) Using Numerical Techniques (Published)
In this work, we present numerical solutions of electrical circuits second-order differential equations which is used as mathematical models of electrical circuits (RLC) consisting of a resistor, an inductor and a capacitor which connected in series and in parallel using numerical approaches. The Differential Transformation Method (DTM) and Exponentially Fitted Collocation Approximation Method (EFCAM) were employed to obtain numerical solutions which were compared with the analytical solutions of the electrical circuits and are found to be accurate and compatible. The graphs for voltages and currents profiles are presented to show the efficiency of numerical technique
Keywords: Differential Transformation Method (DTM), Electrical circuit, Exponentially Fitted Collocation Approximation Method (EFCAM), RLC circuit, analytical solution., currents, voltages