11.Solution of Linear and Nonlinear Partial Differential Equations Using Mixture of Elzaki Transform and the Projected Differential Transform Method (original) (raw)

Solution of Linear and Nonlinear Partial Differential Equations Using

2012

The aim of this study is to solve some linear and nonlinear partial differential equations using the new integral transform "Elzaki transform " and projected differential transform method. The nonlinear terms can be handled by using of projected differential transform method; this method is more efficient and easy to handle such partial differential equations in comparison to other methods. The results show the efficiency and validation of this method.

Solution of partial integro-differential equations by Elzaki transform method

Applied mathematical sciences, 2015

Partial integro-differential equations (PIDE) occur in several fields of sciences and mathematics. The main purpose in this paper for solving partial integrodifferential equation (PIDE) by using a new integral transform Elzaki transform, we convert the proposed PIDE to an ordinary differential equation (ODE) using Elzaki transform (ET), solving this ODE and applying inverse ET an exact solution of the problem is obtained.

Solution of Partial Differential Equations by Elzaki Transform

2018

I n this paper, we introduce a computational algorithm for solving partial differential equations such as Heat Equation, Wave Equation, Laplace Equation and Telegrapher’s Equation etc. by using the modified versions of Laplace and Sumudu transforms which is called Elzaki transform. The Elzaki transform, whose fundamental properties are presented in this paper. Illustrative examples are presented to illustrate the effectiveness of its applicability .

IRJET-Solution of Partial Integro-Differential Equations by using Laplace, Elzaki and Double Elzaki Transform Methods

Partial integro–differential equations (PIDE) occur in several fields of sciences and mathematics. The main purpose of this paper to study how to solve partial integro–differential equation (PIDE) by using various methods like Laplace, Elzaki and Double Elzaki Transform. To solve PIDE by using Laplace Transform (LT), first convert Proposed PIDE to an ordinary differential equation (ODE) then solving this ODE by applying inverse LT we get an exact solution of the problem. To solve PIDE by using Elzaki Transform (ET), first convert Proposed PIDE to an ordinary differential equation (ODE) then solving this ODE by applying inverse ET we get an exact solution of the problem. To solve PIDE by using Double Elzaki Transform (DET), first convert Proposed PIDE to an algebraic equation , Solving this algebraic equation & applying double inverse Elzaki transform we obtain the exact solution of the problem. These methods are useful tools for the solution of the differential and integral equation and linear system of differential and integral equation.

Laplace Projected Differential Transform Method for Solving Nonlinear Partial Differential Equations

This study presents a hybrid method that incorporates Laplace transform along with projected differential transform method to solve partial differential equations which may be utilized to describe physical problems emerging in applied scientific research. Laplace transform is introduced to eliminate the demerit of complex estimation of utilization of differential transform method (DTM) and projected differential method (PDTM). The sufficient condition for the convergence of LPDTM is covered and was applied to solve linear and nonlinear partial differential equations to illustrate the efficiency and dependability of the method. The major advantage of this method is that, the computation comes to be much less complicated to solve and the nonlinear term is effortlessly managed through projected differential transform without utilizing Adomian's polynomial and He's polynomial.

Solution of Ordinary Differential Equation with Initial Condition Using New Elzaki Transform

IRJET, 2023

In this paper the solution of Ordinary Differential Equation with initial condition by using the new Elzaki transform is introduced. The new Elzaki transform is modified version of Laplace and Sumudu transform, and it also expand the nth order derivatives by mathematical induction method. Also in this paper we have explained the properties of Elzaki transform, with inversion form of the transform. With this application we can generate simple formula for solving First order first degree, and Second order first degree ordinary differential equations, with constant coefficients.