desired physical form of cities has been noticeable since the beginning of urbanization, from old patterns of early civilizations to the latest urbanism’s theories, which offered to build better cities. the opinions in recent decades have expressed that compact physical form of cities is a better form than sprawl form to achieve urban sustainability. the form of the city is the embodiment of it...

stefan problem with kinetics is reduced to a system of nonlinear volterra integral equations of second kind and newton's method is applied to linearize it. product integration solution of the linear form is found and sufficient conditions for convergence of the numerical method are given. an example is provided to illustrated the applicability of the method.