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In this paper, a high-order numerical scheme based on quartic B-spline functions is proposed to solve derivative-dependent nonlinear singular boundary value problems. Convergence of the method is analysed. Five test problems are considered to illustrate the accuracy and efficiency of the method. The results obtained by present method are compared with those obtained by the uniform mesh cubic B-spline collocation (UCS) method [P. Roul and V.M.K. Prasad Goura,  B-spline collocation methods and their convergence for a class of nonlinear derivative-dependent singular boundary value problems , Appl. Math. Comput. 341 (2019), pp. 428–450] and non-uniform mesh cubic B-spline collocation (NCS) method [P. Roul and V.M.K. Prasad Goura,  B-spline collocation methods and their convergence for a class of nonlinear derivative-dependent singular boundary value problems , Appl. Math. Comput. 341 (2019), pp. 428–450]. The CPU time of proposed method is compared with that of the NCS method.

A fourth-order numerical method for solving a class of derivative-dependent nonlinear singular boundary value problems