Mumps is one of the diseases that pose global threat to children well-being. In this paper, the problem of the spread of mumps in a closed population is investigated using a SIR compartmental model. Mathematical interpretation of the problem generates nonlinear first-order differential equations. The method of Homotopy Perturbation is adopted to derive the theoretical solutions of the system. Numerical simulations of the analytical results are carried out with the help of Maple 18 software and the solutions are presented in graphical form. The solutions show that Homotopy Perturbation Method (HPM) is an appropriate technique for solving epidemic models.

Application of homotopy perturbation method to an sir mumps model

Numerical methods for solving differential equations  has become an important topic of this era. The importance of  boundary value problems in applied sciences shows the way  in which existence of exact solution is not always possible.  This study adopts the homotopy perturbation method (HPM)  to solve multiple-point boundary value problems arising  in obstacle, unilateral and contact problems. Convergent  approximate solutions are constructed such that the exact  boundary conditions are satisfied. Some examples have been  presented to elucidate the efficiency and implementation of the  method. We have compared the results using different number  of terms of HPM and found that increasing the number of terms  of approximate solution will increase the efficiency.

/pdf/a-study-of-obstacle-problems-using-homotopy-perturbation-3rsgamehoo.pdf

A study of obstacle problems using homotopy perturbation method

This paper proposes an effective improvement of the homotopy perturbation method (HPM) by using Jacobi and He's polynomials to solve some nonlinear ordinary differential equations. With this method, the source terms of ordinary differential equations can be expanded in series of shifted Jacobi polynomials. Numerical results are given in this paper to illustrate the reliability of this method with nonlinear ordinary differential equations.

	Key words: Homotopy perturbation method (HPM), shifted Jacobi polynomials, nonlinear ordinary differential equations.

/pdf/improvement-of-the-homotopy-perturbation-method-to-nonlinear-2tmo7pzghi.pdf

J. F. Alzaidi

Papers

Improvement of the homotopy perturbation method to nonlinear problems