Abstract
The method of bilaterally bounded is using mathematical programming and method of weighted residual to the solution nonlinear differential equation. The method is a semi-exact solution. It is based on collocation method and mathematical programming to create the bilateral inequality. For this process, the differential equation problem will be changed to mathematical programming problem. By using the particle swarm optimization method (PSO), we can get minimum and maximum solution to satisfy inequality. The advantage of the method is that the computer storage cell requirements are less than with the finite element method. A nonlinear differential equation problem is studied as an example. The efficiency, accuracy, and simplicity of this approach are illustrated, indicating that the proposed method can be easily extended to solve a wide range of physical engineering problems.
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