in this paper, the dierential transform method (dtm) is applied to the fisherequation. this method can be used to obtain the exact solutions of fisherequation. finally, we give some examples to illustrate the suciency of themethod for solving such nonlinear partial dierential equations. these resultsshow that this technique is easy to apply.

A Darboux transformation for two new differential-integral equations in the Manakov hierarchy is given by using the gauge transformation between the corresponding matrix spectral problems. As an application of the Darboux transformation, soliton solutions of the two equations are obtained. 1. INTRODUCTION In the past few years, there are extensive development in the area of nonlinear mathematic...

Abstract In this paper, a new form of the homotopy perturbation method (NHPM) has been adopted for solving integro-differential equations. In the present study, firstly the NHPM is used to the integro-differential equation, which yields the Maclaurin series of the exact solution. By applying the Laplace transformation to the truncated Maclaurin series and then the Padé approximation to the solu...

In this study, Lane–Emden complex differential equations have been randomized by selecting random variables for the coefficients, initial conditions, and force functions of equations. addition, finding solutions obtained equations, probability characteristics are examined. The version transformation method (DTM) is used to obtain an analytical solution close equation. Approximate expected value...

In this paper, a proposed computational method referred to as Projected Differential Transformation Method (PDTM) resulting from the modification of the classical Differential Transformation Method (DTM) is applied, for the first time, to the Black–Scholes Equation for European Option Valuation. The results obtained converge faster to their associated exact solution form; these easily computed ...

We use the fractional transformation to convert the nonlinear partial fractional differential equations with the nonlinear ordinary differential equations. The Exp-function method is extended to solve fractional partial differential equations in the sense of the modified Riemann-Liouville derivative. We apply the Exp-function method to the time fractional Sharma-Tasso-Olver equation, the space ...

This study provides an approach to predict the springback phenomenon during post-solidification cooling in a functionally graded hybrid composite cylindrical shell with a transverse isotropic structure. Here, the material properties are given with a general parabolic power-law function. During the theoretical analysis, an appropriate transformation is introduced in the equilibrium equation, whi...

In this paper we propose a new method based on adjoint systems for parametric sensitivity analysis of DAE’s. This method is employed in a series of experiments, and the results are compared with the estimation of sensitivity by a finite differences method, widely used because of the simplicity of its implementation. In addition, we propose a method extension based on the use of estimation funct...

This paper was concerned with studying the magnetohydrodynamic steady laminar free convection flow of a micropolar fluid past a continuously moving surface in the presence of heat generation and thermal radiation. Similarity transformation was employed to transform the governing partial differential equations into ordinary ones, which were then solved numerically using the finite element method...

differential transform method has been applied to solve many functional equations so far. in this article, we have used this method to solve wave-like equations. differential transform method is capable of reducing the size of computational work. exact solutions can also be achieved by the known forms of the series solutions. some examples are prepared to show theefficiency and simplicity of th...