Design of an efficient algorithm for solution of Bratu differential equations

Abstract In this research, we have suggested a combined strategy to calculate and determine the solutions for problems originating in combustion theory and heat transfer, that are known as Bratu differential equations. We aim to suggest and test a soft computing technique using an efficient meta-heuristic the Symbiotic Organism Search (SOS) algorithm and Artificial neural network (ANN) architecture to obtain better solutions for Bratu differential equations by utilizing fewer computational resources and minimal time. We have simulated our computing approach for different cases, and we compare the outcome of our experiments with solutions obtained by the existing state-of-the-art methods. For novelty, we have found an accurate critical value of λc by using SOS algorithm. Values of TIC, MAD, and NSE confirm that our method is a convenient and potential candidate for handling real-application problems. We found that this ANN-SOS algorithm takes less time and is accurate in getting results of the expected standard.