  In this article we deal with the stability and convergence of numerical
solutions of nonlinear evolution equations of the form $A(u(t))+f(u(t))=u'(t)$,
the numerical analysis of solutions to this problems will be performed using
some methods from particular algebras of operators which are sometimes
represented by unital subalgebras of the unital C*-algebras of operators that
are generated by some basic operators say
$\mathbf{1},a,\mathcal{D}(\cdot)\in\mathcal{L}(H^m(G))$ that in some suitable
sense are related to the operator $A(\cdot)\in\mathcal{L}(H^m(G))$ in the
evolution equations, particular cases where the operator algebras do not verify
the C*-identity with respect to the norm chosen are also studied, when
applicable basic C*-algebra techniques are implemented to perform some
estimates of numerical solutions to some types of problems, in all this work
expressions like $H^m(G)$ will represent a prescribed discretizable Hilbert
space with $G\subset\subset\mathbb{R}^n$.
