Developing Clean Technology through Approximate Solutions of Mathematical Models

In this paper, the role of mathematical modeling in the development of clean technology has been considered. One method each for obtaining approximate solutions of mathematical models by ordinary differential equations and partial differential equations respectively arising from the modeling of systems and physical phenomena has been considered. The construction of continuous hybrid methods for the numerical approximation of the solutions of initial value problems of ordinary differential equations as well as homotopy analysis method, an approximate analytical method, for the solution of nonlinear partial differential equations are discussed

Solution of fractional order partial differential equations by discrete homotopy perturbation method

Bu çalışma, lineer ve lineer olmayan zaman kesirli mertebeli kısmi diferensiyel denklemleri çözmek için ayrık uzak biçimli ayrık homotopi perturbasyon metodunu geliştirmiştir. Kesirli mertebe türevler Caputo anlamında göz önüne alınmıştır. Bu metodun başarısı ve uygulanabilirliği bazı örnek problemler ile gösterilmiştir. Elde edilen sonuçlar kesirli mertebe bir olduğunda, tam çözümler ile iyi bir uyumluluk göstermiştir. Bu çalışmada gösterilen metodun kesirli mertebe hesabındaki benzer problemleri çözmesi beklenmektedir.This work is developed the discrete homotopy perturbation method with a space discrete version to solve the linear and nonlinear time derivative fractional partial differential equations. The fractional derivatives are considered in the sense of Caputo. The success and applicability of this method has been demonstrated by some sample problems. When fractional order is unit, obtained results are good agreement with the exact solutions. The method demonstrated in this study is expected to solve similar problems in fractional calcul