A Hybrid Numerical Approach to Solve Multi-singular and Nonlinear Emden–Fowler Equations of Fourth Order: HQLMT

In this research paper, a novel numerical technique called Hermit-quasilinearization matrix technique (HQLMT) is proposed to acquire the approximate solutions of fourth-order multi-singular and nonlinear Emden–Fowler equations. Firstly, the quasilinearization procedure is utilized for the original model problem followed by the application of a collocation method based on the modified version of Hermite functions to the obtained subequations. After the application of the HQLMT, an algebraic system of linear equations is obtained and this system is solved. Hence, the coefficients of the solution form are determined and the approximate solution is obtained. In addition, the error and convergence analysis are studied for the present method. Finally, it is applied to test examples to explain the method and illustrate the efficiency and accuracy of the HQLMT. Simulation results and comparisons with other existing computational methods show that the presented combined technique is an effective approach.