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Consider the following problem related to an ordinary differential equation: 'For given constans ua,ub,M,N, function f(x) in [a,b], find ∂u/∂n at x = a,b which satisfies u"+Mu′+Nu = f in (a,b),u(a) = ua,u(b) = ub'. This kind of problem is called the "Dirichlet-Neumann map problem". This problem is usually solved in two steps. The solution is obtained in the first steps. In the second step, u′(a), u′(b) is computed by differentiating the solution. However, this two-step procedure is inefficient because the solution in (a,b) obtained in the first step is not essentially required. In this paper, the author presents a new strategy for obtaining Neumann data directly via a boundary integral equation formulation. Using this strategy, an explicit analytical expression of the Dirichlet-Neumann map of this problem can be directly obtained by solving 2 × 2 matrices. Furthermore, an extension of the strategy to partial differential equations in two-dimensional space and numerical algorithms is also presented. [ABSTRACT FROM AUTHOR]