The equation ut= Δ u+ up with homogeneous Dirichlet boundary conditions has solutions
with blow-up if p> 1. An adaptive time-step procedure is given to reproduce the asymptotic …

We consider a semilinear parabolic equation with a nonlinear non-dissipative boundary
condition. In the one-dimensional case we describe bifurcation diagrams for positive and …

FULLY DISCRETE ADAPTIVE METHODS FOR A BLOW-UP PROBLEM 1. Introduction We are
interested in develo** fully discrete adaptive nu Page 1 FULLY DISCRETE ADAPTIVE …

In this paper we study numerical approximations for positive solutions of a nonlinear heat
equation with a nonlinear boundary condition. We describe in terms of the nonlinearities …

This paper concerns the study of the numerical approximation for the following
initialboundary value problem\left {u_t-u_ xx= f\left (u\right), x ∈\left (0, 1\right), t ∈\left (0 …

We study numerical approximations to solutions of a system of two nonlinear diffusion
equations in a bounded interval, coupled at the boundary in a nonlinear way. In certain …

We study numerical approximations of positive solutions of the porous medium equation
with a nonlinear source, where m> 1, p> 0 and L> 0 are parameters. We describe in terms of …

We study the asymptotic behavior of a semi-discrete numerical approximation for a pair of
heat equations ut= Δu, vt= Δv in Ω x (0, T); fully coupled by the boundary conditions $\frac …

In this paper we present adaptive procedures for the numerical study of positive solutions of
the following problem: ut= uxx (x, t)∈(0, 1)×[0, T), ux (0, t)= 0 t∈[0, T), ux (1, t)= up (1, t) t∈[0 …

Let be given a parametric polynomial equation system which represents a generically
unramified family of zero-dimensional algebraic varieties. We exhibit an efficient algorithm …