Charles W. Dawson, 47, a government physicist and mathematician who was active in area hiking clubs, died of cancer Jan. 14 at Sibley Memorial Hospital.

He had worked for the David W. Taylor Naval Ship Research and Department Center of the Navy since 1955.

Mr. Dawson was an authority in solving mathematical and computer problems involved in the design of nuclear reactor cores for marine power plants and commercial electric power generation.

He had been director of trails for the Wanderbirds Hiking Club during the early 1970s, and a member of the Potomac Appalachian Trail Club. In 1971 he had completed a solo hike of the entire trail from Georgia to time of his death.

He also belonged to the Archeological Society of Maryland and had served as the organization's vice president in 1976 and as its treasurer for the next two years.

Mr. Dawson was born in Champaign, Ill., and reared in the Washington area. He was a graduate of Laurel High School and the University of Maryland, where he earned a bachelor's degree in physics. He had completed his course work toward a doctoral degree in mathematics at the time of his death.

Survivors include his parents, Walker M. and Emily S. Dawson, both of Beltsville; two sisters, Irene M. Leland of Lansing, Mich., and Ruth E. Phillips of Accokeek, Md.; and three brothers, John M., f Pacific Palisades, Calif., Edward F., of Rockville, and Frederick S., of Sykesville, Md.

The family suggests that expressions of sympathy be in the form of contributions to the Montgomery County Unit of the American Cancer Society.