Hybrid Heuristic Computational approach to the Bratu Problem

In this study a stochastic method based on the heuristic computation is applied for solving the Bratu boundary value problem and an initial value problem of the Bratu-type. A mathematical model consisting of unknown adaptable parameters has been developed using the linear combinations of log sigmoid basis functions. The Genetic algorithm (GA), Pattern Search (PS), Interior Point algorithm (IPA), Active Set algorithm (ASA), and three hybrid schemes combining GA with PS, IPA, and ASA have been employed for learning of the unknown adaptable parameters. To demonstrate the efficacy of the presented method, comparisons of the results are made with the some standard analytical methods as well as the exact solutions. The results from the proposed method are found to be satisfactory and comparable to the standard analytical methods.

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