Controller and control method for internal combustion engine

A non-transitory computer readable recording medium that stores a program that has a processing device execute a control process on an internal combustion engine, the internal combustion engine including an exhaust gas purifier that purifies exhaust gas discharged from a plurality of cylinders and a plurality of fuel injection valves that are respectively provided for the cylinders, the control process comprising:

• executing a dither control process for operating the fuel injection valves in order to set at least one of the cylinders as a rich combustion cylinder and to set at least another one of the cylinders that differs from the at least one of the cylinders as a lean combustion cylinder, wherein the rich combustion cylinder has an air-fuel ratio that is richer than a stoichiometric air-fuel ratio, the lean combustion cylinder has an air-fuel ratio that is leaner than the stoichiometric air-fuel ratio, and a temperature raising capability required for the dither control process in a second mode is higher than that required for the dither control process in a first mode;
• and
• setting a time integration value of the second mode to be greater than a time integration value of the first mode, wherein the time integral value is obtained by time-integrating an absolute value of a difference between the air-fuel ratio of the rich combustion cylinder and the air-fuel ratio of the lean combustion cylinder over a predetermined period.