The numerical solution of time-dependent PDEs is generally based on the FDM technique followed by the method of separating the variables x and t.
Therefore, depending on the geometry of the problem, BC,IC and the source term, the existence, uniqueness and convergence of the solution may or may not be assured.
On the other hand, in the case of the resolution by B-Matrix chains, it is nature itself, represented by its universal laws of physics, which drives its own solution.
It is impossible for nature not to find the appropriate unique fast-converging solution.
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