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Linearization or Discretization: Which To Start With?

When aninfinite dimensional nonlinear equation is to be solved using a computer, thenumerical analyst must decide either to discretize it first and thus topreserve and to transfer the nonlinear aspect to some finite dimensional space,or to linearize it first and then discretize the linear problem. The authors ofthis work have studied both possibilities and have proved the advantages of thesecond option. The talk will show, from a mathematical standpoint, why the approximatesolution obtained by linearizing first and discretizing after, is more accuratethan the one produced when proceeding in the inverse order. Applications toFredholm integral equations of the second kind and to differential spectral problemswill illustrate the theoretical conclusions.
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