Intermittent Problem with Sonata

For several months we have had problems with our Hyundai 2004 Sonata. Because it doesn’t “throw a code”, the dealership can’t find the problem. It doesn’t happen every day–it’s hard for them to catch it misbehaving. Here are the “symptoms”: happens doing in town driving at speeds under 40; jerks and deccelerates, RPM needle jumping around; dies randomly when close to coming to a stop; idles rough at very low RPM sometimes, like it is going to die, other times it idles normally; accelerator acts like it is sticking–engine has accelerated and RPM needle jumped when my foot was not on the brake or gas pedal; if I tap on the accelerator, it calms down (the RPMs go back to normal); seems to do it more when air conditioner is on. Any ideas of what we can have the mechanics look at to fix this? Since it doesn’t throw a code they haven’t done much of anything but throw out ideas. We are very frustrated!

Is the car’s maintenance, including spark plugs, air filter, and fuel filter up to date?

Has the throttle body been cleaned?
Has the Mass Air Flow sensor (MAF) been cleaned?
These are two things that I would recommend if they have not already been done.

Pure guess work: I wonder if it is the throttle position sensor, assuming you Sonata is a drive by wire car.

The air filter and fuel filter are up to date but not sure on the spark plugs–will have them checked out. Also, thanks for the other ideas–the throttle is definitely something we need to have checked out. Today just starting the car in the morning it was like the accelerator pedal stuck–the RPMs went over 4 and the engine raced immediately upon starting. It calmed down when I tapped the accelerator. Thanks for your recommendations!!

Thanks for your thoughts–I am going to have the throttle checked out. Another response mentioned the throttle also. I appreciate your response!