An analysis of several methods for approximately solving the mechanical alloying equation

Abstract

The methods of Picard iteration, power series expansion, perturbation and discretization are applied to a quadratic integrodifferential evolution equation describing an ensemble of particles undergoing concurrent fracture and coalescence. Though the methods are standard, new and improved error bounds and convergence rates are obtained because of the introduction of the total ensemble volume,V₀, into the equation. The problem can then be formulated in function spaces over [o,V₀] instead of [0,∞), permitting much stronger results.

Keywords:

• Coagulation equation
• error bounds
• convergence rates

AMS(MOS)::

• 70–80
• 70F35
• 45K05
• 45L05