Stability and Convergence for Non-Linear Difference Schemes are Equivalent

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Abstract
The Lax-Richtmyer theorem, establishing the equivalence between the stability and convergence of linear difference schemes that are consistent with properly posed linear evolution partial differential equations, is extended to the corresponding general non-linear case, noticing that in the proof of the implication “convergent stable” for the linear case it is possible to avoid using the principle of uniform boundedness of linear operators on Banach spaces.

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