New THE MATHEMATICA JOURNAL article:

Exact and Approximate Solutions of the Abel–Volterra Equations

by JAVAD ABDALKHANI

ABSTRACT: Picard’s iteration is used to find the analytical solutions of some Abel–Volterra equations. For many equations, the integrals involved in Picard’s iteration cannot be evaluated. The author approximates the solutions of those equations employing a semi-implicit product midpoint rule.The Aitken extrapolation is used to accelerate the convergence of both methods. A blow-up phenomena model, a wave propagation, and a superfluity equation are solved to show the practicality of the methods. Programs offered solve the general equations. A user needs only to enter the particular forcing and kernel functions, constants, and a step size for a particular problem.

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