Investors poured money into US stocks yesterday, sending the Dow Jones industrial average up 490.05 points, as the Federal Reserve and other central banks moved to contain the European debt crisis and calm jitters in world financial markets.

But even as the benchmark index rose 4.2 percent - the biggest gain since March 2009 - market watchers questioned whether the action to offer dollars at cheaper rates to foreign banks was a stopgap measure, or the first step toward a solution that would spark a sustained stock rally.

"The market for today at least is highly encouraged,'' said Harvard Business School management professor Robert S. Kaplan, former vice chairman of investment bank Goldman Sachs & Co. "But it's going to be a messy muddle. The markets can deal with a messy muddle that will be scary at times. What they can't deal with is chaos.''

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James T. Swanson, chief investment strategist for Boston mutual funds firm MFS Investment Management, described yesterday's buying surge as a "traders' rally'' that will probably not last.

"Choppiness remains the near-term outlook,'' Swanson said. "This central bank action kicks the can down the road, but it doesn't address the fundamental problem of the unsustainable debt load of the peripheral countries in Europe.''

Rattled by growing fears that the European financial crisis could spiral out of control, a half-dozen government banks around the world yesterday said they would cut in half the cost of a program under which banks in Europe and elsewhere can borrow dollars from central banks. The discount will help the banks fund their own operations and make loans to businesses. The Fed acted in concert with the European Central Bank, the Bank of England, the Bank of Japan, the Swiss National Bank, and the Bank of Canada.

The news pushed the Dow back over the 12,000 mark to close at 12,045.68. With all 30 component stocks rising, the Dow added $142.1 billion in market value yesterday. Other financial markets also rallied, with the tech-heavy Nasdaq exchange jumping 104.83 points, or 4.2 percent, and the Standard & Poor's 500 gaining 51.77 points, or 4.3 percent. Investors were especially eager to snap up bank stocks, which were beaten down in recent months.

But the stock buying binge - which has the Dow ahead by 813.9 points, or 7.2 percent, so far this week - followed a Thanksgiving week retreat that sent the benchmark index down 564.4 points, or 4.8 percent, in one of its worst weekly performances in years.

The dramatic swings are attributable to a series of mixed economic signals, said David Sowerby, portfolio manager for Loomis Sayles & Co., a Boston investment firm. While investors have been heartened by robust third-quarter earnings, surprisingly strong post-Thanksgiving retail sales both in stores and online, and China's move to relax its requirements for banks' cash reserves - making it easier for them to lend money - the uncertainty in Europe points to continued market volatility, Sowerby said.

"It's only Wednesday,'' he said. "After a very strong October, and an up-and-down November that finished flat, you have plenty of reason to expect more of the same.''

Harvard Business School's Kaplan cautioned investors against interpreting yesterday's move to pump money into foreign banks as a signal that Europe had turned the corner and a recovery had begun. But the action by the Fed and other central banks suggested that government and financial leaders are grappling with the challenge, he said. "This would be like the patient being very sick, and we just reduced the chance of one of the complications killing him,'' Kaplan said.

Under the best-case scenario, he said, European banks and governments will agree to a series of moves that will keep credit flowing, but impose austerity measures that force European countries to pay off debt for years into the future. Under the most pessimistic scenario, he said, cooperation among Europe's economic players would collapse, leading to government defaults, bank failures, and frozen credit.

"What the central banks did today is reduce the probability of chaos and dislocations,'' Kaplan said. "It's nerve-racking, but Europe will have to work through this.''

Much will hinge in the short term on whether the greater availability of dollars will help Europe's banks loosen their lending practices, and whether European governments can take other steps to bolster their common currency in the face of slowing growth.

That could mean a largely sideways market for the time being, "until people can be assured that Europe won't drag the US down,'' said Swanson at MFS.

"The overall picture is easing people's fears of a recession in the US,'' he said. "But if Europe continues to weaken, we can't remain insulated from that forever.''

Robert Weisman can be reached at weisman@globe.com.