In this paper‎, ‎first‎, ‎a numerical method is presented for solving a class of linear Fredholm integro-differential equation‎. ‎The operational matrix of derivative is obtained by introducing hybrid third kind Chebyshev polynomials and Block-pulse functions‎. ‎The application of the proposed operational matrix with tau method is then utilized to transform the integro-differential equations to...

The present study introduces a new technique of homotopy perturbation method for the solution of systems of fractional partial differential equations. The proposed scheme is based on Laplace transform and new homotopy perturbation methods. The fractional derivatives are considered in Caputo sense. To illustrate the ability and reliability of the method some examples are provided. The results ob...

In this paper, the reduced dierential transform method is investigated fora nonlinear partial dierential equation modeling nematic liquid crystals, itis called the Hunter-Saxton equation. The main advantage of this methodis that it can be applied directly to nonlinear dierential equations withoutrequiring linearization, discretization, or perturbation. It is a semi analytical-numerical method t...

in this paper, we apply the laplace decomposition method to obtain a series solutions of the burgers-huxley and burgers-fisher equations. the technique is based on the application of laplace transform to nonlinear partial differential equations. the method does not need linearization, weak nonlinearity assumptions or perturbation theory and the nonlinear terms can be easily handled by using the...

In this paper, differential transform method (DTM) is described and is applied to solve systems of nonlinear ordinary differential equations which is arising in HIV infections of cell. Intervals of validity of the solution will be extended by using Pade approximation. The results also will be compared with those results obtained by Runge-Kutta method. The technique is described and is illustrat...

The Multistage Differential Transform Method (MDTM) is employed to solve the model for HIV infection of CD4T cells. Comparing the numerical results to those obtained by the classical fourth order Runge-Kutta method showed the preciseness and efficacy of the multistep differential transform method. The study shows that the method is a powerful and promising tool for solving coupled systems of di...

‎In this article‎, ‎the multi-step conformable fractional differential transform method (MSCDTM) is applied to give approximate solutions of the conformable fractional-order differential systems‎. ‎Moreover‎, ‎we check the stability of conformable fractional-order L\"{u} system with the MSCDTM to demonstrate the efficiency and effectiveness of the proposed procedure.

In this paper, the Chebyshev spectral collocation method(CSCM) for one-dimensional linear hyperbolic telegraph equation is presented. Chebyshev spectral collocation method have become very useful in providing highly accurate solutions to partial differential equations. A straightforward implementation of these methods involves the use of spectral differentiation matrices. Firstly, we transform ...