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Numerical solution of a nonlinear Abel type Volterra integral equation

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  • 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.
    Mathematics Subject Classification: 65R20.

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