Tuition charges at colleges in the Washington area will climb next fall more sharply than in at least a decade, with rises of 15 to 20 percent commonplace and one low-tuition school, the University of the District of Columbia, boosting its rates by 83 percent.

Despite some complaints by students and fears about cutbacks in federal aid, most campuses appear resigned to the increases. Applications to most schools have continued to rise.

Even with its big increase, UDC still will have the area's lowest tuition and required fees -- a total of $364 for city residents. With a 21 percent boost, in-state tuition at the University of Maryland will rise to $1,073. At Catholic University, which is in the middle-range for private colleges, a 16 percent increase will boost tuition over $5,000.

Last January, Maryland's six state colleges -- including Bowie State -- raised tuition 24 percent at the start of the second semester, mostly because of a shortfall in state tax receipts. By next fall tuition at the colleges will be 40 percent higher than it was a year ago.

The new increases far outstrip the general rate of inflation, which was 11.2 percent over the past year, according to the Consumer Price Index released last week by the Labor Department.

"From years we've been trying to protect the students from these horrible increases," said Robert Applegate vice president and treasurer of Catholic University," but we just can't do it anymore. . . . Energy has increased.Labor has increased. We've used up all the reserves we had. We just have to charge more."

"Sure, there's a lot of negative reaction, but people are going to pay," said Charles Dervarics, editor-in-chief of the Hatchet, the student newspaper at George Washington University, where tuition is rising 17 percent to $4,211 next fall. "They'll scrounge up the money somehow. They'll take out more loans. . . . They want to come to this university, an many of their families are middle class and they can sustain an increase."

Tuition, of course, is only part of the bill for attending college. At Catholic U., for example, dorm rooms and meals will average $2,800 next year. cIn addition, officials say students will have to budget about $1,200 for books, miscellaneous expenses and travel, bringing the total cost for a year at Catholic University to just over $9,000. George Washington is about $800 less.

At Georgetown University, the most costly in the area with a tuition of $5,810, average total expenses for undergraduates are expected to reach about $9,600. But even this high figure is substantially below the more than $11,000 annual cost expected at high-prestige schools such as Harvard, Princeton and Stanford, whose tuitions are going up next fall by 14 or 15 percent.

The increases come in the wake of a rapid rise in federal aid to higher education but amid strong doubts about the future of such aid. Since the Middle Income Student Assistance Act of 1978, the amount of low-interest guaranteed loans, which any student can get now regardless of family income, has soared from $2 billion to $4.8 billion a year. Outright grants, based on a needs formula that was considerably liberalized, rose from $1.6 billion to an estimated $2.6 billion this year.

Shortly before the November election, Congress voted to increase aid substantially more. The Reagan administration now is trying to cut it back, mainly by trimming benefits for middle-income families earning $25,000 to $40,000 a year. Many of the college officials interviewed for this article said they thought the proposed cuts might have a severe long-term impact, particularly at high-cost, relatively low-prestige private universities. For next fall, many said their financial aid plans were still uncertain but added that so far they expect no major change in enrollment.

"There's a great deal of concern and anxiety about what's going to happen," said American University president Richard Berendzen. "My personal guess is that the great majority [of students] will be here in the fall, no matter what. Somehow they'll do it out of their own resources."

The number of applicants to American University has increased slightly this year, Berendzen said, even though tuition is rising by 13 percent to $5,240. So far, he reported, a higher proportion of those accepted have said they intend to come to AU.

Berendzen and officials of other local universities said they think schools in the Washington area are in a strong competitive position because of the recent popularity of going to college in big cities and the lure of the capital itself as a center of power. Several said the availability of federal aid had made it easier to increase tuitions.

"I think there's no question about it: the tuition increases have been made possible by the fact that federal aid is readily available, particularly the loans," said Sheldon Knorr, Maryland's commissioner of higher education. t"There's been a real incentive to make costs higher than they might have been because people won't be excluded. It's been a very successful program.

In Maryland, for example, federal grants and loans now total about $250 million a year, Knorr said, and account for more than a third of the tuition paid to public colleges and universities.

Knorr said major tuition increases are required for next fall because tuition hasn't kept pace with inflation over the past two years. At the University of Maryland, for example, tuition rose by 6.6 and 5 percent in 1979 and 1980, less than half the general rate of inflation.

"This year state revenues are down," Knorr said, "and we just had to hold down the state's [spending]."

Even with the increases -- to the $1,073 at the University of Maryland and $1,160 at Bowie State -- the charges for state residents at Maryland's public colleges are still well below those at private schools.

At Virginia's public colleges tuition charges next year also will be slightly more than $1,000 -- George Mason University, for example, will charge $1,008 and the University of Virginia will have a tuition of $1,146. However, the increases in Virginia have been relatively steady during the past few years and next fall they will be considerably less sharp than the major leaps in Maryland. At the University of Virginia the one-year increase is 10 percent; at George Mason, 13.5 percent.

In Washington the severe financial crisis which hit last year led to the steep increase to $364 (from $199 this year) in tuition and required fees at the University of the District of Columbia. The university's enrollment is mostly low-income and when officials voted for the fee hike they said they expected the strain on needy students would be taken care of by increases in federal basic educational opportunity grants, which are tied to tuition costs.

Now they are unsure because President Reagan wants to shave the grant program -- by about 5 percent this year and 10 percent in 1982 -- though administration officials say most low-income students will not be affected.

At Prince George's Community College, where tuition for county residents is going up 22 percent to $572, federal grants and loans were received this year by slightly more than one-third of the students attending at least half-time, said financial aid director Alonia Sharps.

Even so, Sharps said she doesn't expect her college to lose any students because of either the tuition increase or the proposed cutbacks in federal aid.

"I think we may pick up some students," she said. "We will be affordable."

"Last year I think many colleges were afraid to raise tuition as much as they should have," said Timothy Terpstra, assistant dean at Marymount College, a private women's college in Arlington. "But enrollments held. There was plenty of [financial] aid. And this time we felt we could shoot a little higher."

Marymount will raise its tuition 19.4 percent next fall, Terpstra said.

"Maybe all of a sudden this bubble is going to burst," he said. "How much will the public take? . . . But energy is going up. Everything is going up. wWe saw all the other schools doing it [raising tuition], and, of course, that makes it easier to do."