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June  2006, 5(2): 277-288. doi: 10.3934/cpaa.2006.5.277

Numerical solution of a nonlinear Abel type Volterra integral equation

T. Diogo 1, , P. Lima 2, and  M. Rebelo 3,

1. 

Centro de Matematica e Aplicącoes, Instituto Superior Tecnico, Av. Rovisco Pais, 1049-001 Lisboa
2. 

Centro de Matemática Aplicacoes, Instituto Superior Técnico, Av. Rovisco Pais, 1049-001 Lisboa
3. 

Departamento de Matemática, Faculdade de Ciências e Tecnologia, Monte da Caparica, Portugal

Received  March 2005 Revised  June 2005 Published  March 2006

We are concerned with the analytical and numerical analysis of a nonlinear weakly singular Volterra integral equation. Owing to the singularity of the solution at the origin, the global convergence order of Euler's method is less than one. The smoothness properties of the solution are investigated and, by a detailed error analysis, we prove that first order of convergence can be achieved away from the origin. Some numerical results are included confirming the theoretical estimates.
Keywords: Euler's method, Nonlinear Volterra integral equation, weakly singular kernel, convergence..
Mathematics Subject Classification: 65R2.
Citation: T. Diogo, P. Lima, M. Rebelo. Numerical solution of a nonlinear Abel type Volterra integral equation. Communications on Pure and Applied Analysis, 2006, 5 (2) : 277-288. doi: 10.3934/cpaa.2006.5.277
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