Moving fronts and pulses appear in many engineering applications like flame propagation and a falling liquid film. Standard computation methods are inappropriate since the problem is defined over an infinite domain and a steady‐state solution exists only for a certain front velocity. This work presents a transformation that converts the original problem into a boundary‐value problem within a finite domain, in a way that preserves the behavior at the boundaries. Good low‐order approximations can be obtained as demonstrated by two examples. In another approach, a central element of adjustable length is incorporated into a three‐element structure where the edge‐elements obey known asymptotic solutions. That yields multiplicity of travelling fronts in an infinite domain but it successfully approximates standing wave solutions in a finite domain. The approximate solutions are shown to obey the qualitative features known for the exact solutions, like asymptotic solutions or the bifurcation set–the boundary where a new solution emerges or disappears.
|Number of pages||16|
|Journal||Numerical Methods for Partial Differential Equations|
|State||Published - 1990|