APPLICATION OF MULTISTEP REPRODUCING KERNEL HILBERT SPACE METHOD FOR SOLVING GIVING UP SMOKING MODEL
Samia Bushnaq, Banan Maayah, A. AlHabees · International Journal of Pure and Apllied Mathematics · 2016
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 W 2 2 [a, b] 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.