The present work deals with the construction of a high‐order efficient technique for solving one‐dimensional nonlinear Bratu‐type and Lane‐Emden‐type problems describing various physical, chemical and biological phenomena in applied science and engineering. Convergence analysis of the method is studied. Numerical experiments are carried out to demonstrate the efficiency, accuracy and performance of proposed method. The method is shown to have sixth order convergence. The computed results are compared with those obtained by other numerical techniques to justify the advantage of present scheme. It is shown that the proposed method is fast convergent and provides accurate solutions for Bratu‐type and Lane‐Emden‐type problems with low computational cost.
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