A note on the solution of singular boundary value problems arising in engineering and applied sciences: Use of OHAM

Many problems of physical and engineering sciences are described by singular boundary value problems (SBVPs). Due to the presence of singularity, these problems pose difficulties in obtaining their solutions, and various solution schemes have been proposed to overcome these difficulties. The present work is concerned with the application of one such recently developed method, namely optimal homotopy analysis method (OHAM), to solve SBVPs. The OHAM has certain advantages: (i) it is a general method, (ii) contains an adjustable parameter to control the convergence of solution, and (iii) for certain choices of auxiliary quantities, its working resembles with those of other similar methods.The effectiveness of the OHAM has been evaluated by successfully solving two SBVPs given in recent literature as well a SBVP related to the reaction–diffusion process in a spherical catalyst. The obtained results for these problems show an excellent agreement when compared with the numerical/exact/available solutions.

► OHAM has been applied to solve singular boundary value problems.
► An adjustable parameter controls the convergence of solution in OHAM.
► Results of MADM can be obtained as a special case.