In this paper we apply the idea of Dixon resultant to algebraic differential equations and introduce the Dixon differential resultant. We prove that a necessary condition for the existence of a common solution of two algebraic differential equations is that the differential resultant is equal to zero, which actually provides a method of elimination and reduces a system of multi-variate differen...

This work deals with the three-dimensional magneto-thermo-elastic problem of a functionally graded truncated conical shell under non-uniform internal pressure and subjected to magnetic and thermal fields. The material properties are assumed to obey the power law form that depends on the thickness coordinate of the shell. The formulation of the problem begins with the derivation of fundamental r...

In this paper, an effective numerical method is introduced for the treatment of nonlinear two-dimensional Volterra-Fredholm integro-differential equations. Here, we use the so-called two-dimensional block-pulse functions.First, the two-dimensional block-pulse operational matrix of integration and differentiation has been presented. Then, by using this matrices, the nonlinear two-dimensional Vol...

In this paper, we propose a method to approximate the solution of a linear Fredholm integro-differential equation by using the Chebyshev wavelet of the first kind as basis. For this purpose, we introduce the first Chebyshev operational matrix of integration. Chebyshev wavelet approximating method is then utilized to reduce the integro-differential equation to a system of algebraic equations. Il...

The purpose of this study is to develop a new approach in modeling and simulation of a reverse osmosis desalination system by using fractional differential equations. Using the Legendre wavelet method combined with the decoupling and quasi-linearization technique, we demonstrate the validity and applicability of our model. Examples are developed to illustrate the fractional differential techniq...

In this paper, an effective numerical method is introduced for the treatment of nonlinear two-dimensional Volterra-Fredholm integro-differential equations. Here, we use the so-called two-dimensional block-pulse functions.First, the two-dimensional block-pulse operational matrix of integration and differentiation has been presented. Then, by using this matrices, the nonlinear two-dimensional Vol...

a modified f-expansion method to find the exact traveling wave solutions of  two-component nonlinear partial differential equations (nlpdes) is discussed. we use this method to construct many new solutions to the nonlinear whitham-broer-kaup system (1+1)-dimensional. the solutions obtained include jacobi elliptic periodic wave solutions which exactly degenerate to the soliton solutions, triangu...

In this paper, a  fuzzy numerical procedure for solving fuzzy linear Volterra integro-differential equations of the second kind under strong  generalized differentiability is designed. Unlike the existing numerical methods, we do not replace the original fuzzy equation by a $2times 2$ system ofcrisp equations, that is the main difference between our method  and other numerical methods.Error ana...

in this paper, the stability and boundedness of solutions of a second order nonlinear vectordifferential equation are investigated. our results include and improve some well-known results in therelevant literature.