Engine fuel control apparatus, method and computer program product

In the case that an engine is operated in a state where an in-cylinder air/fuel ratio is lean in a stratified combustion region (I) and a fuel cut control is performed under a predetermined condition, when catalysts 32, 34 are in a low temperature state where a purification performance is deteriorated or when a NOx absorptive amount of the lean NOx catalyst 34, to devise a control procedure for exhaust air/fuel state at a recovery timing from the fuel cut control so that a driving feeling is improved while maintaining the exhaust purification performance by the catalysts 32, 34. When the fuel cut control is terminated and the engine 1 shifts into the stratified combustion region (I) (SA14), if a catalyst temperature Tcat is at or below a set temperature Tcat1 or a NOx absorptive amount Snox is at or above a set amount S2 (SA16, SA17), the in-cylinder air/fuel ratio of the engine 1 is correctively enriched and the exhaust air/fuel state is enriched.