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The present paper deals with the designation of a new efficient numerical scheme for numerical solution of a class of coupled systems of Emden-Fowler equations describing several processes in applied sciences and technology. This method combines the shifted version of airfoil functions of the first kind (AFFK) and quasilinearization technique. More specifically, the quasilinearization technique is first applied to the original problem and the shifted AFFK (SAFFK) collocation matrix technique is then constructed for obtaining the solution of resulting family of submodels. We derive the error bound and analyze the convergence properties of the SAFFK. Computational and experimental simulations are carried out to describe the applicability and accuracy of the new technique. To show the benefit of the new approach, the computed numerical outcomes are compared with those results obtained via the Bernoulli and Haar wavelets collocation methods. It is evident from the numerical illustrations that the new developed scheme is superior to the existing available ones. The elapsed CPU time of the proposed method is provided. [ABSTRACT FROM AUTHOR]

This work concerns with a novel computational approach to solve a two‐dimensional Caputo time‐fractional convection reaction–diffusion (CTFCRD) equation with the weak singularity at the initial time. In this method, the L1$$ L1 $$‐scheme on graded mesh is used to approximate the Caputo temporal derivative, while the spatial derivatives are approximated by using a compact finite difference method (CFDM) coupled with alternating direction implicit (ADI) scheme. We present a methodology to examine the optimal error estimates of the proposed scheme, in terms of L2$$ {L}^2 $$‐norm. Convergence and stability results are proved. It is shown that the suggested method yields an optimal order, that is, min(2‐ β$$ \beta $$, aβ$$ a\beta $$, 2 β$$ \beta $$+1) in time direction, where β$$ \beta $$ is the order of time fractional derivative and a$$ a $$ is the grading parameter and has a fourth‐order of convergence in space direction. Finally, two numerical examples are provided to verify the theoretical estimates and to illustrate the accuracy and efficiency of the method. [ABSTRACT FROM AUTHOR]