ABSTRACT
This chapter shows the application of the Trefftz-Herrera collocation method [1-3] to obtain the numerical solution of nonstandard boundary value problems with prescribed jumps (BVPJ) which arise when the systematic modeling approach for continuum systems is applied to model the dynamics of combustion fronts in porous media [4]. Up to now, collocation has been applied by means of splines. However, a broader and more efficient formulation is obtained when collocation is applied using fully discontinuous functions by means of the indirect (or Trefftz-Herrera) methodology. The Trefftz-Herrera approach is a very general theory of domain decomposition methods (DDM), proposed by Herrera [5] and stemming from Trefftz method. When the TrefftzHerrera approach is applied in combination with orthogonal collocation, it produces a family of non-standard collocation methods known as ‘‘indirect collocation’’ or ‘‘TH-collocation methods’’.
