Critical Exponents of Semilinear Equations via the Feynman-Kac Formula

2000 Mathematics Subject Classification: 60H30, 35K55, 35K57, 35B35.

Numerical Simulation of Stochastic Di erential Equations

Stochastic differential equation (SDE) is a differential equation in which some of the terms and its solution are stochastic processes. SDEs play a central role in modeling physical systems like finance, Biology, Engineering, to mention some. In modeling process, the computation of the trajectories (sample paths) of solutions to SDEs is very important. However, the exact solution to a SDE is generally difficult to obtain due to non-differentiability character of realizations of the Brownian motion. There exist approximation methods of solutions of SDE. The solutions will be continuous stochastic processes that represent diffusive dynamics, a common modeling assumption for financial, Biology, physical, environmental systems. This Masters' thesis is an introduction and survey of numerical solution methods for stochastic differential equations. Standard numerical methods, local linearization methods and filtering methods are well described. We compute the root mean square errors for each method from which we propose a better numerical scheme. Stochastic differential equations can be formulated from a given ordinary differential equations. In this thesis, we describe two kind of formulations: parametric and non-parametric techniques. The formulation is based on epidemiological SEIR model. This methods have a tendency of increasing parameters in the constructed SDEs, hence, it requires more data. We compare the two techniques numerically.

Semi-Smooth Newton Methods for the Time Optimal Control of Nonautonomous Ordinary Differential Equations

AMS Subj. Classification: 49J15, 49M15

A Numerical method for the semilinear stochastic transport equation

Trabalho apresentado no XXXV CNMAC, Natal-RN, 2014.

Um estudo do teorema de unicidade de Holmgren

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Continuidade de atratores para a discretização de problemas parabólicos usando o método de elementos finitos

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Um estudo sobre a equação de Schrödinger biharmônica

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Gevrey Local Solvability for Semilinear Partial Differential Equations

2002 Mathematics Subject Classification: 35S05

Solving Differential Equations by Parallel Laplace Method with Assured Accuracy

The paper has been presented at the 12th International Conference on Applications of Computer Algebra, Varna, Bulgaria, June, 2006

Pseudo-almost periodic solutions for abstract partial functional differential equations

In this work we study the existence and uniqueness of pseudo-almost periodic solutions for a first-order abstract functional differential equation with a linear part dominated by a Hille-Yosida type operator with a non-dense domain. (C) 2009 Published by Elsevier Ltd

Controllability results for impulsive mixed type functional integro-differential evolution equations with nonlocal conditions

In this paper, we establish the controllability for a class of abstract impulsive mixed-type functional integro-differential equations with finite delay in a Banach space. Some sufficient conditions for controllability are obtained by using the Mönch fixed point theorem via measures of noncompactness and semigroup theory. Particularly, we do not assume the compactness of the evolution system. An example is given to illustrate the effectiveness of our results.

Semigrupos de operadores lineares e equações diferenciais em espaços de Banach

Pós-graduação em Matemática Universitária - IGCE

Semigrupos de operadores lineares e aplicações

Pós-graduação em Matemática Universitária - IGCE

Detecção e localização de descargas parciais em transformadores de potência utilizando sinais acústicoas transitórios e o método GSPS

Neste trabalho, é desenvolvido um método de localização de descargas parciais, em transformadores de potência, baseado no algoritmo GPS (Global Positioning System). Para a análise da estrutura, foi desenvolvido um solftware, no qual as equações diferenciais que representam a propagação de ondas acústicas são resolvidas numericamente através do método Acoustic Finite Difference Time Domain (AFDTD), cujo domínio computacional é truncado através da técnica CPML (Convolutional Perfectly Matched Layer). Os resultados obtidos são comparados a estimativas produzidas utilizando-se sinais elétricos relativos às descargas.

Existence and Uniqueness of Solutions for Partial Differential-Functional Equations of the First Order with Deviating Argument of the Derivative of Unknown Function

We consider the existence and uniqueness problem for partial differential-functional equations of the first order with the initial condition for which the right-hand side depends on the derivative of unknown function with deviating argument.