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In this article we deal with the stability and convergence of numericalsolutions 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 usingsome methods from particular algebras of operators which are sometimesrepresented by unital subalgebras of the unital C*-algebras of operators thatare generated by some basic operators say$\mathbf{1},a,\mathcal{D}(\cdot)\in\mathcal{L}(H^m(G))$ that in some suitablesense are related to the operator $A(\cdot)\in\mathcal{L}(H^m(G))$ in theevolution equations, particular cases where the operator algebras do not verifythe C*-identity with respect to the norm chosen are also studied, whenapplicable basic C*-algebra techniques are implemented to perform someestimates of numerical solutions to some types of problems, in all this workexpressions like $H^m(G)$ will represent a prescribed discretizable Hilbertspace with $G\subset\subset\mathbb{R}^n$.

On the Approximation of Nonlinear Evolution Equations in Particular C*-Algebras of Operators