Samia Bushnaq, Banan Maayah, Asma AlHabees
Department of Basic Sciences
King Abdullah II Faculty of Engineering
Princess Sumaya University for Technology
Amman 11941, JORDAN
Department of Mathematics
Faculty of Science
The University of Jordan
Amman 11942, JORDAN

Abstract. Smoking is the leading avoidable cause of death in the world. In this paper, we apply the Reproducing Kernel Hilbert Space method on the giving up smoking model to find an approximate solution of the model then we compare it with the fourth order Runge-Kutta method. The solutions are represented in the form of series in the Hilbert space with easily computable components. In finding the computational solutions, we use generating the orthogonal basis from the obtained kernel functions such that the orthonormal basis is constructing in order to formulate and utilize the solutions. Numerical experiments are carried where two smooth reproducing kernel functions are used throughout the evolution of the algorithm to obtain the required nodal values of the unknown variables. The utilized graphical results show that the present algorithm and simulated annealing provide a good scheduling methodology to such model.

Received: May 9, 2016

AMS Subject Classification: 65L05, 65L06

Key Words and Phrases: reproducing kernel Hilbert space method (RKHSM), giving up smoking model, numerical solution

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