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Master's Dissertation
DOI
10.11606/D.55.2018.tde-19092018-145039
Document
Author
Full name
José Luiz de Souza
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 1992
Supervisor
Committee
Franco, Neide Maria Bertoldi (President)
Meneguette Junior, Messias
Pereira, Aldenice Brito
Title in Portuguese
Extensão natural contínua dos métodos de Runge-Kutta para equações integrais de Volterra de segunda espécie e suas aplicações
Keywords in Portuguese
Não disponível
Abstract in Portuguese
O principal propósito deste trabalho e estudar a estrutura dos métodos de Runge-Kutta para equações integrais de Volterra. Isto tem sido desenvolvido de forma tradicional durante vários anos. Este assunto será tratado com uma roupagem bem atual, a qual necessita da teoria de grafos, tornando assim mais fácil a tarefa de obtenção dos coeficientes de Volterra-Runge-Kutta. Também estão incluídas as extensões naturais continuas do mesmo método, de modo a mostrar que e possível construir funções polinomiais continuas por partes, de ordem suficientemente elevada, as quais permitem estender a aproximação nos pontos da malha para todo intervalo de integração.
Title in English
Natural continuous extensions of Runge-Kutta methods for Volterra integral equations of the second kind and their applications
Keywords in English
Not availabe
Abstract in English
The mean purpose of this work is to study the structure of Runge-Kutta methods for Volterra Integral Equations. This has been developped for many years in a classical way. This matter will be treated in a very recent fashion, which needs Theory of Graphs, becoming the task of getting Volterra-Runge-Kutta coefficents very easy. Also, it is included the so called Natural Continuous Extensions of the same method, in order to show that, it is possible to build sufficent high order piecewise polynomial functions, which allow to extend the approximation at the grid points, to the whole interval of integration.
 
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JoseLuizdeSouza.pdf (2.67 Mbytes)
Publishing Date
2018-09-19
 
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