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In this paper, we study a numerical approximation for the following localized nonlinear reaction-difiusion equation ... where f(s) is a positive, increasing, c² R convex function for the nonnegative values of s, ... We find some conditions under which the solution of a discrete form of the above problem blows up in a finite time and estimate its discrete blow-up time. We also prove the convergence of the numerical blow-up time to the theoretical one. Finally, we give some numerical results to illustrate our analysis. [ABSTRACT FROM AUTHOR]

In this paper, we consider the following initial-boundary problem ... where Ω is a bounded domain in RN with smooth boundary Ω L is an elliptic operator, where initial data in which our initial energy can take positive values, with initial and boundary conditions of Dirichlet type, and the nonlinear function f(s) is a positive, increasing and convex function for the nonnegative values of s and b, ξ is a positive parameter. This work is concerned with a nonlinear wave equation with nonlinear source terms acting in this equation. We will prove that the solution of our considered problem blows up in finite time provided that the initial data and the parameter ξ are small enough. Under some assumptions, we show that the solution of the above problem blows up in a finite time and its blow-up time goes to the one of the solution of the following differential equations ... Finally, we give some numerical results to illustrate our analysis. [ABSTRACT FROM AUTHOR]