in mathematics, a type of method for the solution of problems of mathematical analysis. Usually classed as direct methods are methods for solving, for example, differential equations, integral equations, integro-differential equations, and variational problems by means of the construction of a sequence of functions (or systems of functions) that converge to the solution of a simpler problem; this simpler problem generally, in the limit, coincides with the given problem. Direct methods are used most often for the approximate solution of problems in mathematical analysis. They are sometimes also used to find exact solutions and to prove existence theorems for solutions.

Examples of direct methods are finite-difference methods for solving differential, integral, and integro-differential equations; the Euler method for solving problems in the calculus of variations; the Ritz method and the method of steepest descents, which are used to solve variational problems and problems that reduce to variational problems; and the Galerkin method, which is used to solve many boundary-value problems, including those that do not reduce to variational problems.