تفاصيل الرسالة العلمية

In this thesis, a residual power series method (RPS) is proposed to find out the series solutions to strongly linear and nonlinear systems of fuzzy initial value problems (IVPs). The new method is effective and easy to use for solving linear and nonlinear systems of FIVPs without linearization, perturbation, or discretization. This method constructs an analytical approximate solutions in the form of a polynomial which obtains Taylor expansion of the solutions. The solutions obtained using the present method are tested against the exact solutions by solving two linear and one nonlinear problems. Graphical results, tabulate data, and numerical comparisons are presented and discussed quantitatively to illustrate the fuzzy solutions. Numerical results show the potentiality, the generality, and the superiority of our algorithm for solving such fuzzy equations. This new method promises to open new possibilities for applications in an important class of uncertain physical, engineering, and economical problems