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In this paper, we use He's homotopy perturbation method (HPM) for solving linear programming (LP) problems. By applying HPM for this class of problems, optimal solutions of a primal LP problem and its corresponding dual problem can be obtained at the same time. The efficiency of the method is shown by solving some examples. [ABSTRACT FROM AUTHOR]

In this paper we propose a new approach for solving linear and nonlinear Volterra integral equations (LVIE, NVIE) of the first and the second kinds. First, we define a new problem in calculus of variations, which is equivalent to this kind of problem. By taking this approach, one can solve a large number of problems in calculus of variations. We use a discretisation method to obtain a nonlinear programming problem and in some cases a linear programming problem. Then by using the optimal solution of the latest (LP or NLP) problem, we obtain an approximate solution with a controllable error for the original solution. [ABSTRACT FROM AUTHOR]