THE REAGAN administration appears to be working out a smooth solution to a dispute, over F15 jet fighters for Saudi Arabia, that tied the previous administration in knots. It was not for lack of trying but Jimmy Carter never succeeded in extricating the issue from a context in which it seemed that providing the planes would be a victory for the Saudis and a defeat for the Israelis. In that context, the issue was murder, diplomatically and politically, too.

Ronald Reagan, however, seems to be finding a new and more fluid context. Evidently he will sell the Saudis the F15 fuel tanks and bomb racks that they have sought to improve their defenses and to test their relationship with Washington. At the same time, he is seeking material and political ways to compensate the Israelis for adding to an Arab neighbor's attack capability and for breaking the Carter plege not to sell the Saudis the extra gear. He is doing this, however, without a public battle.

The interesting question is whether his handling of the F15 issue can or will be a model for his handling of the Arab-Israeli dispute overall. There is reason to believe Mr. Reagan sees it in just those terms. He does not accept that the American commitment to Israel and the American interest in improving relations with the Arab states are mutually exclusive. On the contrary, he sees them as consistent and reinforcing, especially in view of the danger posed by Soviet support of radical currents in the area.

The president has the substantial advantage of starting out enjoying Israel's confidence. He does not have to prove himself constantly on that score. The Arab side, meanwhile, seems ready to give him the benefit of the doubt. The F15 question had assumed an extraordinary symbolic importance among the Saudis and their friends, and they are bound to appreciate the Reagan approach to it.

With the F15 equation solved, Mr. Reagan's first need will be to make sure that the diplomatic stage is not cluttered by the European Mideast initiative that Britian's Margaret Thatcher is about to try to sell to the new administration before the leaders of Egypt and Israel get to town. The Europeans would jettison the whole Camp David framework and open a new negotiation in which the PLO would be invited to take part, without first having to accept Israel, and would be offered the option of a state on the pre-1967 lines in two years' time.

Why is Mrs. Thatcher, or her foreign secretary, so bent on undermining the existing negotiating framework, which has already produced one Arab-Israeli peace treaty and which is still available for further diplomatic exploitation, particularly if a new Israeli government comes to power? Mrs. Thatcher will be here at the end of the month to explain her government's position. The Reagan administration will want to hear her out, but it must then get down to the serious business of figuring out how it can capitalize on the good start provided by its F15 decision.