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Neural network optimized with evolutionary computing technique for solving the 2-dimensional Bratu problem
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| Organization: | International Islamic University |
| Department: | Department of Electronic Engineering |
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| Neural Computing & Applications |
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In this paper, a stochastic technique is developed to solve 2-dimensional Bratu equations using feedforward artificial neural networks, optimized with genetic and interior-point algorithms. The 2-dimensional equations are first transformed into a 1-dimensional boundary value problem, and a mathematical model of the transformed equation is then formulated with neural networks using an unsupervised error. Network weights are optimized to minimize the error. Evolutionary computing based on genetic algorithms is used as a tool for global search, integrated with an interior-point method for rapid local convergence. The methodology is applied to solve three cases of boundary value problems for the Bratu equations. The accuracy, convergence and effectiveness of the scheme is validated for a large number of simulations. Comparison of results is made with the exact solution derived using MATHEMATICA, and is found to be in good agreement.
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2-Dimensional Bratu equations Neural, networks Genetic algorithms Nonlinear ODEs Hybrid, techniques Interior-point methods
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