This paper presents a fifth-order iterative method as a new modification of Newton's method for finding multiple roots of nonlinear equations with unknown multiplicity m. Its convergence order is analyzed and proved. Moreover, several numerical examples demonstrate that the proposed iterative method is superior to the existing methods. We consider the… (More)
In this paper, we consider a semilinear parabolic equation u t = ∆u + u q t 0 u p (x, s)ds, x ∈ Ω, t > 0 with nonlocal nonlinear boundary condition u| ∂Ω×(0,+∞) = Ω ϕ(x, y)u l (y, t)dy and nonnegative initial data, where p, q ≥ 0 and l > 0. The blow-up criteria and the blow-up rate are obtained.