Numerical solution of a nonlinear Abel type Volterra integral equation

T. Diogo; P. Lima; M. Rebelo

doi:10.3934/cpaa.2006.5.277

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2006, Volume 5, Issue 2: 277-288. Doi: 10.3934/cpaa.2006.5.277

This issue Previous Article The numerical solution of weakly singular Volterra functional integro-differential equations with variable delays Next Article Comparison of numerical methods for fractional differential equations

Numerical solution of a nonlinear Abel type Volterra integral equation

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

Received: March 2005

Revised: June 2005

Published: June 2006

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Abstract

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.

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Mathematics Subject Classification: 65R20.

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