The Dow Jones industrial average gained 109.26 points, 0.81 percent, and closed at 13,676.23. The Standard & Poor's 500 showed a 13.27-point gain, 0.88 percent, to 1,519.60. The Nasdaq composite index improved 45.33 points, 1.65 percent, to 2,799.26.
"It was a good earnings day, and investors may have been anticipating more good earnings after the close," Stephen Carl, Williams Capital head trader, told The Wall Street Journal.
Apple reported a 67 percent increase in quarterly profit. However, the Richmond, Va., Federal Reserve's manufacturing index for October fell to minus 5 from 14 in September. Numbers below zero indicate contraction in activity.
On the New York Stock Exchange 2,204 stocks rose and 1,061 declined, on volume of 3.3 billion shares.
The U.S. Treasury 10-year note rose 31.25 cents for every $1,000 invested to yield 4.409 percent.
The euro was at $1.4261 from $1.4164 against the dollar Monday. The dollar was at 114.89 yen from 114.30 yen Monday.
Britain's FTSE 100 Index rose 1.5 percent to 6,558.80.
Japan's Nikkei 225 average closed up 0.07 percent at 16,450.58 points.