Combined Laplace Transform-Homotopy Perturbation Method for Sine-Gordon Equation

In this paper, the combined Laplace transform-homotopy perturbation method C(LT-HPM) is presented and used to solve the initial value problem for the sine-Gordon equation to obtain the approximate-exact solutions. The results obtained show the reliability and the efficiency of this method

Solving the coupled Schrödinger -Korteweg- de-Vries system by modified variational iteration method with genetic algorithm

 A system of nonlinear partial differential equations was solved using a modified variational iteration method (MVIM) combined with a genetic algorithm. The modified method introduced an auxiliary parameter (p) in the correction functional to ensure convergence and improve the outcomes. Before applying the modification, the traditional variational iteration method (VIM) was used firstly. The method was applied to numerically solve the system of Schrödinger-KdV equations. By comparing the two methods in addition to some of the previous approaches, it turns out the new algorithm converges quickly, generates accurate solutions and shows improved accuracy. Additionally, the method can be easily applied to various linear and nonlinear differential equations

Histiocytoid Sweet Syndrome associated with anorectal lymphogranuloma venereum in a patient with HIV infection

Sweet Syndrome belongs to a group of diseases known as neutrophilic dermatoses. An uncommon variant named Histiocytoid Sweet Syndrome (HSS) can be associated with a variety of conditions, including cancer, infections, drug toxicity and others. Here we present an instance of HSS in an HIV-positive patient in an infectious disease settin

On the applicability of the Adomian method to initial value problems with discontinuities

AbstractIn this paper we extend our results of L. Casasús, W. Al-Hayani [The decomposition method for ordinary differential equations with discontinuities, Appl. Math. Comput. 131 (2002) 245–251] to initial value problems with several types of discontinuities, giving relevant examples of linear and nonlinear cases

Solutions of Singular IVP’s of Lane-Emden type by Homotopy analysis method with Genetic Algorithm

In this paper, Homotopy Analysis Method with Genetic Algorithm is presented and used for solving Lane-Emden type singular initial value problems. The method is demonstrated for a variety of problems where approximate-exact solutions are obtained. The results obtained in all cases show the reliability and the efficiency of this metho