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Made available in DSpace on 2014-06-11T19:22:18Z (GMT). No. of bitstreams: 0 Previous issue date: 2012-02-27Bitstream added on 2014-06-13T20:28:32Z : No. of bitstreams: 1 santos_gr_me_sjrp.pdf: 399304 bytes, checksum: 6932f6a8d97705e593070d265e935262 (MD5) / Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) / Este trabalho tem como objetivo aplicar o método das aproximações sucessivas na demonstração do Teorema do ponto fixo de Banach e em resultados que garantem a existência e unicidade de soluções de equações diferenciais definidas em espaços de Banach / This work aims to apply the method of successive approximations in the proof of Banach fixed point Theorem and in results that guarantee the existence and uniqueness of solutions of differential equations defined in Banach spaces

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Under some conditions in real world, precise parameters and/or initial values of dynamic systems are hard to be determined. Fuzzy Differential Equation (FDE) is a powerful tool to model dynamical systems with the uncertainty of impreciseness. This thesis presents the first numerical solution for Fuzzy Differential Equations with multiple fuzzy parameters and initial Values (FDEPIV) problems. Previous approaches for solving the FDEs only focused on FDEs with single fuzzy condition. In this thesis, we applied the proper fuzzy arithmetic on Runge-Kutta method for solving the FDEPIV problems with multiple fuzzy parameters and initial conditions. Furthermore, comparing with directly applying the extension principle in solving FDEPIV, the complexity of the proposed method is much lower, and parallelization of the proposed algorithm is feasible. Numerical examples of the FDEPIV problems are presented to demonstrate the effectiveness of the proposed method.

Under some conditions in real world, precise parameters and/or initial values of dynamic systems are hard to be determined. Fuzzy Differential Equation (FDE) is a powerful tool to model dynamical systems with the uncertainty of impreciseness. This thesis presents the first numerical solution for Fuzzy Differential Equations with multiple fuzzy parameters and initial Values (FDEPIV) problems. Previous approaches for solving the FDEs only focused on FDEs with single fuzzy condition. In this thesis, we applied the proper fuzzy arithmetic on Runge-Kutta method for solving the FDEPIV problems with multiple fuzzy parameters and initial conditions. Furthermore, comparing with directly applying the extension principle in solving FDEPIV, the complexity of the proposed method is much lower, and parallelization of the proposed algorithm is feasible. Numerical examples of the FDEPIV problems are presented to demonstrate the effectiveness of the proposed method.

Thesis (M.A.)--Boston University / The problem of finding the solution to a general eliptic type partial differential equation, when the boundary values are given, is generally referred to as the Dirichlet Problem. In this paper I consider the special eliptic equation of ∇2 J=0 which is Laplace's equation, and I limit myself to the case of two dimensions. Subject to these limitations I discuss five proofs for the existence of a solution to Laplace's equation for arbitrary regions where the boundary values are given. [TRUNCATED]

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In the category of mathematics called partial differential equations there is a particular type of problem called the Dirichlet problem. Proof is given in many partial differential equation books that every Dirichlet problem has one and only one solution. The explicit solution is very often not easily determined, so that a method for approximating the solution at certain points becomes desirable. The purpose of this paper is to present and investigate one such method.